Hypothesis

Postnatal environmental exposures, particularly those found in household products and dietary intake, along with specific serum metabolomics profiles, are significantly associated with the BMI Z-score of children aged 6-11 years. Higher concentrations of certain metabolites in serum, reflecting exposure to chemical classes or metals, will correlate with variations in BMI Z-score, controlling for age and other relevant covariates. Some metabolites associated with chemical exposures and dietary patterns can serve as biomarkers for the risk of developing obesity.

Background

Research indicates that postnatal exposure to endocrine-disrupting chemicals (EDCs) such as phthalates, bisphenol A (BPA), and polychlorinated biphenyls (PCBs) can significantly influence body weight and metabolic health (Junge et al., 2018). These chemicals, commonly found in household products and absorbed through dietary intake, are linked to detrimental effects on body weight and metabolic health in children. This hormonal interference can lead to an increased body mass index (BMI) in children, suggesting a potential pathway through which exposure to these chemicals contributes to the development of obesity.

A longitudinal study on Japanese children examined the impact of postnatal exposure (first two years of life) to p,p’-dichlorodiphenyltrichloroethane (p,p’-DDT) and p,p’-dichlorodiphenyldichloroethylene (p,p’-DDE) through breastfeeding (Plouffe et al., 2020). The findings revealed that higher levels of these chemicals in breast milk were associated with increased BMI at 42 months of age. DDT and DDE may interfere with hormonal pathways related to growth and development. These chemicals can mimic or disrupt hormones that regulate metabolism and fat accumulation. This study highlights the importance of understanding how persistent organic pollutants can affect early childhood growth and development.

The study by Harley et al. (2013) investigates the association between prenatal and postnatal Bisphenol A (BPA) exposure and various body composition metrics in children aged 9 years from the CHAMACOS cohort. The study found that higher prenatal BPA exposure was linked to a decrease in BMI and body fat percentages in girls but not boys, suggesting sex-specific effects. Conversely, BPA levels measured at age 9 were positively associated with increased adiposity in both genders, highlighting the different impacts of exposure timing on childhood development.

The 2022 study 2022 study by Uldbjerg et al. explored the effects of combined exposures to multiple EDCs, suggesting that mixtures of these chemicals can have additive or synergistic effects on BMI and obesity risk. Humans are typically exposed to a mixture of chemicals rather than individual EDCs, making it crucial to understand how these mixtures might interact. The research highlighted that the interaction between different EDCs can lead to additive (where the effects simply add up) or even synergistic (where the combined effect is greater than the sum of their separate effects) outcomes. These interactions can significantly amplify the risk factors associated with obesity and metabolic disorders in children. The dose-response relationship found that even low-level exposure to multiple EDCs could result in significant health impacts due to their combined effects.

These studies collectively illustrate the critical role of environmental EDCs in shaping metabolic health outcomes in children, highlighting the necessity for ongoing research and policy intervention to mitigate these risks.

Data Description

This study will utilize data from the subcohort of 1301 mother-child pairs in the HELIX study, who are which aged 6-11 years for whom complete exposure and outcome data were available. Exposure data included detailed dietary records after pregnancy and concentrations of various chemicals like BPA and PCBs in child blood samples. There are categorical and numerical variables, which will include both demographic details and biochemical measurements. This dataset allows for robust statistical analysis to identify potential associations between EDC exposure and changes in BMI Z-scores, considering confounding factors such as age, gender, and socioeconomic status. There are no missing data so there is not need to impute the information. Child BMI Z-scores were calculated based on WHO growth standards.

load("/Users/allison/Library/CloudStorage/GoogleDrive-aflouie@usc.edu/My Drive/HELIX_data/HELIX.RData")
filtered_chem_diet <- codebook %>%
  filter(domain %in% c("Chemicals", "Lifestyles") & period == "Postnatal" & subfamily != "Allergens")

# specific covariates
filtered_covariates <- codebook %>%
  filter(domain == "Covariates" & 
         variable_name %in% c("ID", "e3_sex_None", "e3_yearbir_None", "h_edumc_None", "h_cohort", "hs_child_age_None"))

#specific phenotype variables
filtered_phenotype <- codebook %>%
  filter(domain == "Phenotype" & 
         variable_name %in% c("hs_zbmi_who"))

# combining all necessary variables together
combined_codebook <- bind_rows(filtered_chem_diet, filtered_covariates, filtered_phenotype)
kable(combined_codebook, align = "c", format = "html") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)
variable_name domain family subfamily period location period_postnatal description var_type transformation labels labelsshort
h_bfdur_Ter h_bfdur_Ter Lifestyles Lifestyle Diet Postnatal NA NA Breastfeeding duration (weeks) factor Tertiles Breastfeeding Breastfeeding
hs_bakery_prod_Ter hs_bakery_prod_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: bakery products (hs_cookies + hs_pastries) factor Tertiles Bakery prod BakeProd
hs_beverages_Ter hs_beverages_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: beverages (hs_dietsoda+hs_soda) factor Tertiles Soda Soda
hs_break_cer_Ter hs_break_cer_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: breakfast cereal (hs_sugarcer+hs_othcer) factor Tertiles BF cereals BFcereals
hs_caff_drink_Ter hs_caff_drink_Ter Lifestyles Lifestyle Diet Postnatal NA NA Drinks a caffeinated or æenergy drink (eg coca-cola, diet-coke, redbull) factor Tertiles Caffeine Caffeine
hs_dairy_Ter hs_dairy_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: dairy (hs_cheese + hs_milk + hs_yogurt+ hs_probiotic+ hs_desert) factor Tertiles Dairy Dairy
hs_fastfood_Ter hs_fastfood_Ter Lifestyles Lifestyle Diet Postnatal NA NA Visits a fast food restaurant/take away factor Tertiles Fastfood Fastfood
hs_KIDMED_None hs_KIDMED_None Lifestyles Lifestyle Diet Postnatal NA NA Sum of KIDMED indices, without index9 numeric None KIDMED KIDMED
hs_mvpa_prd_alt_None hs_mvpa_prd_alt_None Lifestyles Lifestyle Physical activity Postnatal NA NA Clean & Over-reporting of Moderate-to-Vigorous Physical Activity (min/day) numeric None PA PA
hs_org_food_Ter hs_org_food_Ter Lifestyles Lifestyle Diet Postnatal NA NA Eats organic food factor Tertiles Organicfood Organicfood
hs_proc_meat_Ter hs_proc_meat_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: processed meat (hs_coldmeat+hs_ham) factor Tertiles Processed meat ProcMeat
hs_readymade_Ter hs_readymade_Ter Lifestyles Lifestyle Diet Postnatal NA NA Eats a æready-made supermarket meal factor Tertiles Ready made food ReadyFood
hs_sd_wk_None hs_sd_wk_None Lifestyles Lifestyle Physical activity Postnatal NA NA sedentary behaviour (min/day) numeric None Sedentary Sedentary
hs_total_bread_Ter hs_total_bread_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: bread (hs_darkbread+hs_whbread) factor Tertiles Bread Bread
hs_total_cereal_Ter hs_total_cereal_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: cereal (hs_darkbread + hs_whbread + hs_rice_pasta + hs_sugarcer + hs_othcer + hs_rusks) factor Tertiles Cereals Cereals
hs_total_fish_Ter hs_total_fish_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: fish and seafood (hs_canfish+hs_oilyfish+hs_whfish+hs_seafood) factor Tertiles Fish Fish
hs_total_fruits_Ter hs_total_fruits_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: fruits (hs_canfruit+hs_dryfruit+hs_freshjuice+hs_fruits) factor Tertiles Fruits Fruits
hs_total_lipids_Ter hs_total_lipids_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: Added fat factor Tertiles Diet fat Diet fat
hs_total_meat_Ter hs_total_meat_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: meat (hs_coldmeat+hs_ham+hs_poultry+hs_redmeat) factor Tertiles Meat Meat
hs_total_potatoes_Ter hs_total_potatoes_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: potatoes (hs_frenchfries+hs_potatoes) factor Tertiles Potatoes Potatoes
hs_total_sweets_Ter hs_total_sweets_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: sweets (hs_choco + hs_sweets + hs_sugar) factor Tertiles Sweets Sweets
hs_total_veg_Ter hs_total_veg_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: vegetables (hs_cookveg+hs_rawveg) factor Tertiles Vegetables Vegetables
hs_total_yog_Ter hs_total_yog_Ter Lifestyles Lifestyle Diet Postnatal NA NA Food group: yogurt (hs_yogurt+hs_probiotic) factor Tertiles Yogurt Yogurt
hs_dif_hours_total_None hs_dif_hours_total_None Lifestyles Lifestyle Sleep Postnatal NA NA Total hours of sleep (mean weekdays and night) numeric None Sleep Sleep
hs_as_c_Log2 hs_as_c_Log2 Chemicals Metals As Postnatal NA NA Arsenic (As) in child numeric Logarithm base 2 As As
hs_cd_c_Log2 hs_cd_c_Log2 Chemicals Metals Cd Postnatal NA NA Cadmium (Cd) in child numeric Logarithm base 2 Cd Cd
hs_co_c_Log2 hs_co_c_Log2 Chemicals Metals Co Postnatal NA NA Cobalt (Co) in child numeric Logarithm base 2 Co Co
hs_cs_c_Log2 hs_cs_c_Log2 Chemicals Metals Cs Postnatal NA NA Caesium (Cs) in child numeric Logarithm base 2 Cs Cs
hs_cu_c_Log2 hs_cu_c_Log2 Chemicals Metals Cu Postnatal NA NA Copper (Cu) in child numeric Logarithm base 2 Cu Cu
hs_hg_c_Log2 hs_hg_c_Log2 Chemicals Metals Hg Postnatal NA NA Mercury (Hg) in child numeric Logarithm base 2 Hg Hg
hs_mn_c_Log2 hs_mn_c_Log2 Chemicals Metals Mn Postnatal NA NA Manganese (Mn) in child numeric Logarithm base 2 Mn Mn
hs_mo_c_Log2 hs_mo_c_Log2 Chemicals Metals Mo Postnatal NA NA Molybdenum (Mo) in child numeric Logarithm base 2 Mo Mo
hs_pb_c_Log2 hs_pb_c_Log2 Chemicals Metals Pb Postnatal NA NA Lead (Pb) in child numeric Logarithm base 2 Pb Pb
hs_tl_cdich_None hs_tl_cdich_None Chemicals Metals Tl Postnatal NA NA Dichotomous variable of thallium (Tl) in child factor None Tl Tl
hs_dde_cadj_Log2 hs_dde_cadj_Log2 Chemicals Organochlorines DDE Postnatal NA NA Dichlorodiphenyldichloroethylene (DDE) in child adjusted for lipids numeric Logarithm base 2 DDE DDE
hs_ddt_cadj_Log2 hs_ddt_cadj_Log2 Chemicals Organochlorines DDT Postnatal NA NA Dichlorodiphenyltrichloroethane (DDT) in child adjusted for lipids numeric Logarithm base 2 DDT DDT
hs_hcb_cadj_Log2 hs_hcb_cadj_Log2 Chemicals Organochlorines HCB Postnatal NA NA Hexachlorobenzene (HCB) in child adjusted for lipids numeric Logarithm base 2 HCB HCB
hs_pcb118_cadj_Log2 hs_pcb118_cadj_Log2 Chemicals Organochlorines PCBs Postnatal NA NA Polychlorinated biphenyl -118 (PCB-118) in child adjusted for lipids numeric Logarithm base 2 PCB 118 PCB118
hs_pcb138_cadj_Log2 hs_pcb138_cadj_Log2 Chemicals Organochlorines PCBs Postnatal NA NA Polychlorinated biphenyl-138 (PCB-138) in child adjusted for lipids numeric Logarithm base 2 PCB 138 PCB138
hs_pcb153_cadj_Log2 hs_pcb153_cadj_Log2 Chemicals Organochlorines PCBs Postnatal NA NA Polychlorinated biphenyl-153 (PCB-153) in child adjusted for lipids numeric Logarithm base 2 PCB 153 PCB153
hs_pcb170_cadj_Log2 hs_pcb170_cadj_Log2 Chemicals Organochlorines PCBs Postnatal NA NA Polychlorinated biphenyl-170 (PCB-170) in child adjusted for lipids numeric Logarithm base 2 PCB 170 PCB170
hs_pcb180_cadj_Log2 hs_pcb180_cadj_Log2 Chemicals Organochlorines PCBs Postnatal NA NA Polychlorinated biphenyl-180 (PCB-180) in child adjusted for lipids numeric Logarithm base 2 PCB 180 PCB180
hs_sumPCBs5_cadj_Log2 hs_sumPCBs5_cadj_Log2 Chemicals Organochlorines PCBs Postnatal NA NA Sum of PCBs in child adjusted for lipids (4 cohorts) numeric Logarithm base 2 PCBs SumPCB
hs_dep_cadj_Log2 hs_dep_cadj_Log2 Chemicals Organophosphate pesticides DEP Postnatal NA NA Diethyl phosphate (DEP) in child adjusted for creatinine numeric Logarithm base 2 DEP DEP
hs_detp_cadj_Log2 hs_detp_cadj_Log2 Chemicals Organophosphate pesticides DETP Postnatal NA NA Diethyl thiophosphate (DETP) in child adjusted for creatinine numeric Logarithm base 2 DETP DETP
hs_dmdtp_cdich_None hs_dmdtp_cdich_None Chemicals Organophosphate pesticides DMDTP Postnatal NA NA Dichotomous variable of dimethyl dithiophosphate (DMDTP) in child factor None DMDTP DMDTP
hs_dmp_cadj_Log2 hs_dmp_cadj_Log2 Chemicals Organophosphate pesticides DMP Postnatal NA NA Dimethyl phosphate (DMP) in child adjusted for creatinine numeric Logarithm base 2 DMP DMP
hs_dmtp_cadj_Log2 hs_dmtp_cadj_Log2 Chemicals Organophosphate pesticides DMTP Postnatal NA NA Dimethyl thiophosphate (DMTP) in child adjusted for creatinine numeric Logarithm base 2 DMDTP DMTP
hs_pbde153_cadj_Log2 hs_pbde153_cadj_Log2 Chemicals Polybrominated diphenyl ethers (PBDE) PBDE153 Postnatal NA NA Polybrominated diphenyl ether-153 (PBDE-153) in child adjusted for lipids numeric Logarithm base 2 PBDE 153 PBDE153
hs_pbde47_cadj_Log2 hs_pbde47_cadj_Log2 Chemicals Polybrominated diphenyl ethers (PBDE) PBDE47 Postnatal NA NA Polybrominated diphenyl ether-47 (PBDE-47) in child adjusted for lipids numeric Logarithm base 2 PBDE 47 PBDE47
hs_pfhxs_c_Log2 hs_pfhxs_c_Log2 Chemicals Per- and polyfluoroalkyl substances (PFAS) PFHXS Postnatal NA NA Perfluorohexane sulfonate (PFHXS) in child numeric Logarithm base 2 PFHXS PFHXS
hs_pfna_c_Log2 hs_pfna_c_Log2 Chemicals Per- and polyfluoroalkyl substances (PFAS) PFNA Postnatal NA NA Perfluorononanoate (PFNA) in child numeric Logarithm base 2 PFNA PFNA
hs_pfoa_c_Log2 hs_pfoa_c_Log2 Chemicals Per- and polyfluoroalkyl substances (PFAS) PFOA Postnatal NA NA Perfluorooctanoate (PFOA) in child numeric Logarithm base 2 PFOA PFOA
hs_pfos_c_Log2 hs_pfos_c_Log2 Chemicals Per- and polyfluoroalkyl substances (PFAS) PFOS Postnatal NA NA Perfluorooctane sulfonate (PFOS) in child numeric Logarithm base 2 PFOS PFOS
hs_pfunda_c_Log2 hs_pfunda_c_Log2 Chemicals Per- and polyfluoroalkyl substances (PFAS) PFUNDA Postnatal NA NA Perfluoroundecanoate (PFUNDA) in child numeric Logarithm base 2 PFUNDA PFUNDA
hs_bpa_cadj_Log2 hs_bpa_cadj_Log2 Chemicals Phenols BPA Postnatal NA NA Bisphenol A (BPA) in child adjusted for creatinine numeric Logarithm base 2 BPA BPA
hs_bupa_cadj_Log2 hs_bupa_cadj_Log2 Chemicals Phenols BUPA Postnatal NA NA N-Butyl paraben (BUPA) in child adjusted for creatinine numeric Logarithm base 2 BUPA BUPA
hs_etpa_cadj_Log2 hs_etpa_cadj_Log2 Chemicals Phenols ETPA Postnatal NA NA Ethyl paraben (ETPA) in child adjusted for creatinine numeric Logarithm base 2 ETPA ETPA
hs_mepa_cadj_Log2 hs_mepa_cadj_Log2 Chemicals Phenols MEPA Postnatal NA NA Methyl paraben (MEPA) in child adjusted for creatinine numeric Logarithm base 2 MEPA MEPA
hs_oxbe_cadj_Log2 hs_oxbe_cadj_Log2 Chemicals Phenols OXBE Postnatal NA NA Oxybenzone (OXBE) in child adjusted for creatinine numeric Logarithm base 2 OXBE OXBE
hs_prpa_cadj_Log2 hs_prpa_cadj_Log2 Chemicals Phenols PRPA Postnatal NA NA Propyl paraben (PRPA) in child adjusted for creatinine numeric Logarithm base 2 PRPA PRPA
hs_trcs_cadj_Log2 hs_trcs_cadj_Log2 Chemicals Phenols TRCS Postnatal NA NA Triclosan (TRCS) in child adjusted for creatinine numeric Logarithm base 2 TRCS TRCS
hs_mbzp_cadj_Log2 hs_mbzp_cadj_Log2 Chemicals Phthalates MBZP Postnatal NA NA Mono benzyl phthalate (MBzP) in child adjusted for creatinine numeric Logarithm base 2 MBZP MBZP
hs_mecpp_cadj_Log2 hs_mecpp_cadj_Log2 Chemicals Phthalates MECPP Postnatal NA NA Mono-2-ethyl 5-carboxypentyl phthalate (MECPP) in child adjusted for creatinine numeric Logarithm base 2 MECPP MECPP
hs_mehhp_cadj_Log2 hs_mehhp_cadj_Log2 Chemicals Phthalates MEHHP Postnatal NA NA Mono-2-ethyl-5-hydroxyhexyl phthalate (MEHHP) in child adjusted for creatinine numeric Logarithm base 2 MEHHP MEHHP
hs_mehp_cadj_Log2 hs_mehp_cadj_Log2 Chemicals Phthalates MEHP Postnatal NA NA Mono-2-ethylhexyl phthalate (MEHP) in child adjusted for creatinine numeric Logarithm base 2 MEHP MEHP
hs_meohp_cadj_Log2 hs_meohp_cadj_Log2 Chemicals Phthalates MEOHP Postnatal NA NA Mono-2-ethyl-5-oxohexyl phthalate (MEOHP) in child adjusted for creatinine numeric Logarithm base 2 MEOHP MEOHP
hs_mep_cadj_Log2 hs_mep_cadj_Log2 Chemicals Phthalates MEP Postnatal NA NA Monoethyl phthalate (MEP) in child adjusted for creatinine numeric Logarithm base 2 MEP MEP
hs_mibp_cadj_Log2 hs_mibp_cadj_Log2 Chemicals Phthalates MIBP Postnatal NA NA Mono-iso-butyl phthalate (MiBP) in child adjusted for creatinine numeric Logarithm base 2 MIBP MIBP
hs_mnbp_cadj_Log2 hs_mnbp_cadj_Log2 Chemicals Phthalates MNBP Postnatal NA NA Mono-n-butyl phthalate (MnBP) in child adjusted for creatinine numeric Logarithm base 2 MNBP MNBP
hs_ohminp_cadj_Log2 hs_ohminp_cadj_Log2 Chemicals Phthalates OHMiNP Postnatal NA NA Mono-4-methyl-7-hydroxyoctyl phthalate (OHMiNP) in child adjusted for creatinine numeric Logarithm base 2 OHMiNP OHMiNP
hs_oxominp_cadj_Log2 hs_oxominp_cadj_Log2 Chemicals Phthalates OXOMINP Postnatal NA NA Mono-4-methyl-7-oxooctyl phthalate (OXOMiNP) in child adjusted for creatinine numeric Logarithm base 2 OXOMINP OXOMINP
hs_sumDEHP_cadj_Log2 hs_sumDEHP_cadj_Log2 Chemicals Phthalates DEHP Postnatal NA NA Sum of DEHP metabolites (µg/g) in child adjusted for creatinine numeric Logarithm base 2 DEHP SumDEHP
FAS_cat_None FAS_cat_None Chemicals Social and economic capital Economic capital Postnatal NA NA Family affluence score factor None Family affluence FamAfl
hs_contactfam_3cat_num_None hs_contactfam_3cat_num_None Chemicals Social and economic capital Social capital Postnatal NA NA scoial capital: family friends factor None Social contact SocCont
hs_hm_pers_None hs_hm_pers_None Chemicals Social and economic capital Social capital Postnatal NA NA How many people live in your home? numeric None House crowding HouseCrow
hs_participation_3cat_None hs_participation_3cat_None Chemicals Social and economic capital Social capital Postnatal NA NA social capital: structural factor None Social participation SocPartic
hs_cotinine_cdich_None hs_cotinine_cdich_None Chemicals Tobacco Smoke Cotinine Postnatal NA NA Dichotomous variable of cotinine in child factor None Cotinine Cotinine
hs_globalexp2_None hs_globalexp2_None Chemicals Tobacco Smoke Tobacco Smoke Postnatal NA NA Global exposure of the child to ETS (2 categories) factor None ETS ETS
hs_smk_parents_None hs_smk_parents_None Chemicals Tobacco Smoke Tobacco Smoke Postnatal NA NA Tobacco Smoke status of parents (both) factor None Smoking_parents SmokPar
e3_sex_None e3_sex_None Covariates Covariates Child covariate Pregnancy NA NA Child sex (female / male) factor None Child sex Sex
e3_yearbir_None e3_yearbir_None Covariates Covariates Child covariate Pregnancy NA NA Year of birth (2003 to 2009) factor None Year of birth YearBirth
h_cohort h_cohort Covariates Covariates Maternal covariate Pregnancy NA NA Cohort of inclusion (1 to 6) factor None Cohort Cohort
h_edumc_None h_edumc_None Covariates Covariates Maternal covariate Pregnancy NA NA Maternal education (1: primary school, 2:secondary school, 3:university degree or higher) factor None Maternal education mEducation
hs_child_age_None hs_child_age_None Covariates Covariates Child covariate Postnatal NA NA Child age at examination (years) numeric None Child age cAge
hs_zbmi_who hs_zbmi_who Phenotype Phenotype Outcome at 6-11 years old Postnatal NA NA Body mass index z-score at 6-11 years old - WHO reference - Standardized on sex and age numeric None Body mass index z-score zBMI

Data Summary for Exposures, Covariates, and Outcome

Data Summary Exposures: Lifestyles

# specific lifestyle exposures
lifestyle_exposures <- c(
  "h_bfdur_Ter",
  "hs_bakery_prod_Ter",
  "hs_break_cer_Ter",
  "hs_dairy_Ter",
  "hs_fastfood_Ter",
  "hs_org_food_Ter",
  "hs_proc_meat_Ter",
  "hs_total_fish_Ter",
  "hs_total_fruits_Ter",
  "hs_total_lipids_Ter",
  "hs_total_sweets_Ter",
  "hs_total_veg_Ter"
)

lifestyle_exposome <- dplyr::select(exposome, all_of(lifestyle_exposures))
summarytools::view(dfSummary(lifestyle_exposome, style = 'grid', plain.ascii = FALSE, valid.col = FALSE, headings = FALSE), method = "render")
No Variable Stats / Values Freqs (% of Valid) Graph Missing
1 h_bfdur_Ter [factor]
1. (0,10.8]
2. (10.8,34.9]
3. (34.9,Inf]
506(38.9%)
270(20.8%)
525(40.4%)
 0 (0.0%)
2 hs_bakery_prod_Ter [factor]
1. (0,2]
2. (2,6]
3. (6,Inf]
345(26.5%)
423(32.5%)
533(41.0%)
 0 (0.0%)
3 hs_break_cer_Ter [factor]
1. (0,1.1]
2. (1.1,5.5]
3. (5.5,Inf]
291(22.4%)
521(40.0%)
489(37.6%)
 0 (0.0%)
4 hs_dairy_Ter [factor]
1. (0,14.6]
2. (14.6,25.6]
3. (25.6,Inf]
359(27.6%)
465(35.7%)
477(36.7%)
 0 (0.0%)
5 hs_fastfood_Ter [factor]
1. (0,0.132]
2. (0.132,0.5]
3. (0.5,Inf]
143(11.0%)
603(46.3%)
555(42.7%)
 0 (0.0%)
6 hs_org_food_Ter [factor]
1. (0,0.132]
2. (0.132,1]
3. (1,Inf]
429(33.0%)
396(30.4%)
476(36.6%)
 0 (0.0%)
7 hs_proc_meat_Ter [factor]
1. (0,1.5]
2. (1.5,4]
3. (4,Inf]
366(28.1%)
471(36.2%)
464(35.7%)
 0 (0.0%)
8 hs_total_fish_Ter [factor]
1. (0,1.5]
2. (1.5,3]
3. (3,Inf]
389(29.9%)
454(34.9%)
458(35.2%)
 0 (0.0%)
9 hs_total_fruits_Ter [factor]
1. (0,7]
2. (7,14.1]
3. (14.1,Inf]
413(31.7%)
407(31.3%)
481(37.0%)
 0 (0.0%)
10 hs_total_lipids_Ter [factor]
1. (0,3]
2. (3,7]
3. (7,Inf]
397(30.5%)
403(31.0%)
501(38.5%)
 0 (0.0%)
11 hs_total_sweets_Ter [factor]
1. (0,4.1]
2. (4.1,8.5]
3. (8.5,Inf]
344(26.4%)
516(39.7%)
441(33.9%)
 0 (0.0%)
12 hs_total_veg_Ter [factor]
1. (0,6]
2. (6,8.5]
3. (8.5,Inf]
404(31.1%)
314(24.1%)
583(44.8%)
 0 (0.0%)

Generated by summarytools 1.0.1 (R version 4.4.0)
2024-07-09

categorical_lifestyle <- lifestyle_exposome %>% 
  dplyr::select(where(is.factor))

categorical_lifestyle_long <- pivot_longer(
  categorical_lifestyle,
  cols = everything(),
  names_to = "variable",
  values_to = "value"
)

unique_categorical_vars <- unique(categorical_lifestyle_long$variable)
categorical_plots <- lapply(unique_categorical_vars, function(var) {
  data <- filter(categorical_lifestyle_long, variable == var)
  
  p <- ggplot(data, aes(x = value, fill = value)) +
    geom_bar(stat = "count") +
    labs(title = paste("Distribution of", var), x = var, y = "Count")
  
  print(p)
  return(p)
})

Breastfeeding Duration: Majority of observations are in the highest duration category, suggesting longer breastfeeding periods are common.

Bakery Products: Shows a relatively even distribution across the three categories, indicating varied consumption levels of bakery products among participants.

Breakfast Cereal: The highest category of cereal consumption is the most common, suggesting a preference for or greater consumption of cereals.

Dairy: Shows a fairly even distribution across all categories, indicating a uniform consumption pattern of dairy products.

Fast Food: Most participants fall into the middle category, indicating moderate consumption of fast food.

Organic Food: Most participants either consume a lot of or no organic food, with fewer in the middle range.

Processed Meat: Consumption levels are fairly evenly distributed, indicating varied dietary habits regarding processed meats.

Bread: Distribution shows a significant leaning towards higher bread consumption.

Cereal: Even distribution across categories suggests varied cereal consumption habits.

Fish and Seafood: Even distribution across categories, indicating varied consumption of fish and seafood.

Fruits: High fruit consumption is the most common, with fewer participants in the lowest category.

Added Fats: More participants consume added fats at the lowest and highest levels, with fewer in the middle.

Sweets: High consumption of sweets is the most common, indicating a preference for or higher access to sugary foods.

Vegetables: Most participants consume a high amount of vegetables.

Data Summary Exposures: Chemicals

# specific chemical exposures
chemical_exposures <- c(
  "hs_cd_c_Log2",
  "hs_co_c_Log2",
  "hs_cs_c_Log2",
  "hs_cu_c_Log2",
  "hs_hg_c_Log2",
  "hs_mo_c_Log2",
  "hs_pb_c_Log2",
  "hs_dde_cadj_Log2",
  "hs_pcb153_cadj_Log2",
  "hs_pcb170_cadj_Log2",
  "hs_dep_cadj_Log2",
  "hs_pbde153_cadj_Log2",
  "hs_pfhxs_c_Log2",
  "hs_pfoa_c_Log2",
  "hs_pfos_c_Log2",
  "hs_prpa_cadj_Log2",
  "hs_mbzp_cadj_Log2",
  "hs_mibp_cadj_Log2",
  "hs_mnbp_cadj_Log2"
)

chemical_exposome <- dplyr::select(exposome, all_of(chemical_exposures))
summarytools::view(dfSummary(chemical_exposome, style = 'grid', plain.ascii = FALSE, valid.col = FALSE, headings = FALSE), method = "render")
No Variable Stats / Values Freqs (% of Valid) Graph Missing
1 hs_cd_c_Log2 [numeric]
Mean (sd) : -4 (1)
min ≤ med ≤ max:
-10.4 ≤ -3.8 ≤ 0.8
IQR (CV) : 1 (-0.3)
 695 distinct values 0 (0.0%)
2 hs_co_c_Log2 [numeric]
Mean (sd) : -2.3 (0.6)
min ≤ med ≤ max:
-5.5 ≤ -2.4 ≤ 1.4
IQR (CV) : 0.7 (-0.3)
 317 distinct values 0 (0.0%)
3 hs_cs_c_Log2 [numeric]
Mean (sd) : 0.4 (0.6)
min ≤ med ≤ max:
-1.5 ≤ 0.5 ≤ 3.1
IQR (CV) : 0.8 (1.3)
 369 distinct values 0 (0.0%)
4 hs_cu_c_Log2 [numeric]
Mean (sd) : 9.8 (0.2)
min ≤ med ≤ max:
9.1 ≤ 9.8 ≤ 12.1
IQR (CV) : 0.3 (0)
 345 distinct values 0 (0.0%)
5 hs_hg_c_Log2 [numeric]
Mean (sd) : -0.3 (1.7)
min ≤ med ≤ max:
-10.9 ≤ -0.2 ≤ 3.7
IQR (CV) : 2.1 (-5.6)
 698 distinct values 0 (0.0%)
6 hs_mo_c_Log2 [numeric]
Mean (sd) : -0.3 (0.9)
min ≤ med ≤ max:
-9.2 ≤ -0.4 ≤ 5.1
IQR (CV) : 0.8 (-2.9)
 593 distinct values 0 (0.0%)
7 hs_pb_c_Log2 [numeric]
Mean (sd) : 3.1 (0.6)
min ≤ med ≤ max:
1.1 ≤ 3.1 ≤ 7.7
IQR (CV) : 0.8 (0.2)
 529 distinct values 0 (0.0%)
8 hs_dde_cadj_Log2 [numeric]
Mean (sd) : 4.7 (1.5)
min ≤ med ≤ max:
1.2 ≤ 4.5 ≤ 11.1
IQR (CV) : 1.9 (0.3)
 1050 distinct values 0 (0.0%)
9 hs_pcb153_cadj_Log2 [numeric]
Mean (sd) : 3.6 (0.9)
min ≤ med ≤ max:
1.2 ≤ 3.5 ≤ 7.8
IQR (CV) : 1.4 (0.3)
 1047 distinct values 0 (0.0%)
10 hs_pcb170_cadj_Log2 [numeric]
Mean (sd) : -0.3 (3)
min ≤ med ≤ max:
-16.8 ≤ 0.3 ≤ 4.8
IQR (CV) : 2.2 (-9.8)
 1039 distinct values 0 (0.0%)
11 hs_dep_cadj_Log2 [numeric]
Mean (sd) : 0.2 (3.2)
min ≤ med ≤ max:
-12.6 ≤ 0.9 ≤ 9.4
IQR (CV) : 3.3 (20)
 1045 distinct values 0 (0.0%)
12 hs_pbde153_cadj_Log2 [numeric]
Mean (sd) : -4.5 (3.8)
min ≤ med ≤ max:
-17.6 ≤ -2.6 ≤ 4
IQR (CV) : 6.7 (-0.8)
 1036 distinct values 0 (0.0%)
13 hs_pfhxs_c_Log2 [numeric]
Mean (sd) : -1.6 (1.3)
min ≤ med ≤ max:
-8.9 ≤ -1.4 ≤ 4.8
IQR (CV) : 1.7 (-0.8)
 1061 distinct values 0 (0.0%)
14 hs_pfoa_c_Log2 [numeric]
Mean (sd) : 0.6 (0.6)
min ≤ med ≤ max:
-2.2 ≤ 0.6 ≤ 2.7
IQR (CV) : 0.7 (0.9)
 1061 distinct values 0 (0.0%)
15 hs_pfos_c_Log2 [numeric]
Mean (sd) : 1 (1.1)
min ≤ med ≤ max:
-10.4 ≤ 1 ≤ 5.1
IQR (CV) : 1.3 (1.1)
 1050 distinct values 0 (0.0%)
16 hs_prpa_cadj_Log2 [numeric]
Mean (sd) : -1.6 (3.8)
min ≤ med ≤ max:
-12 ≤ -2.3 ≤ 10.8
IQR (CV) : 5.2 (-2.4)
 1031 distinct values 0 (0.0%)
17 hs_mbzp_cadj_Log2 [numeric]
Mean (sd) : 2.4 (1.2)
min ≤ med ≤ max:
-0.6 ≤ 2.3 ≤ 7.2
IQR (CV) : 1.5 (0.5)
 1046 distinct values 0 (0.0%)
18 hs_mibp_cadj_Log2 [numeric]
Mean (sd) : 5.5 (1.1)
min ≤ med ≤ max:
2.3 ≤ 5.4 ≤ 9.8
IQR (CV) : 1.5 (0.2)
 1057 distinct values 0 (0.0%)
19 hs_mnbp_cadj_Log2 [numeric]
Mean (sd) : 4.7 (1)
min ≤ med ≤ max:
1.9 ≤ 4.6 ≤ 8.9
IQR (CV) : 1.3 (0.2)
 1048 distinct values 0 (0.0%)

Generated by summarytools 1.0.1 (R version 4.4.0)
2024-07-09

#separate numeric and categorical data
numeric_chemical <- chemical_exposome %>% 
  dplyr::select(where(is.numeric))

numeric_chemical_long <- pivot_longer(
  numeric_chemical,
  cols = everything(),
  names_to = "variable",
  values_to = "value"
)

unique_numerical_vars <- unique(numeric_chemical_long$variable)

num_plots <- lapply(unique_numerical_vars, function(var) {
  data <- filter(numeric_chemical_long, variable == var)
  p <- ggplot(data, aes(x = value)) +
    geom_histogram(bins = 30, fill = "blue") +
    labs(title = paste("Histogram of", var), x = "Value", y = "Count")
  print(p)
  return(p)
})

Cadmium (hs_cd_c_Log2): The distribution of cadmium levels is skewed to the right, indicating that most participants have lower exposure levels, with a few cases showing significantly higher exposures.

Cobalt (hs_co_c_Log2): The histogram of cobalt levels displays a roughly normal distribution centered around a slight positive skew. This suggests a common source of exposure with varying levels among the population.

Cesium (hs_cs_c_Log2): Exhibits a right-skewed distribution, indicating that most participants have relatively low exposure levels, but a small number have substantially higher exposures.

Copper (hs_cu_c_Log2): Shows a right-skewed distribution, suggesting that while most individuals have moderate exposure, a few experience significantly higher levels of copper.

Mercury (hs_hg_c_Log2): This distribution is also right-skewed, common for environmental pollutants, where a majority have lower exposure levels, and a minority have high exposure levels.

Molybdenum (hs_mo_c_Log2): Shows a distribution with a sharp peak and a long right tail, suggesting that while most people have similar exposure levels, a few have exceptionally high exposures.

Lead (hs_pb_c_Log2): The distribution is slightly right-skewed, indicating higher exposure levels in a smaller group of the population compared to the majority.

DDE (hs_dde_cadj_Log2): Shows a pronounced right skew, typical for chemicals that accumulate in the environment and in human tissues, indicating higher levels of exposure in a smaller subset of the population..

PCB 153 (hs_pcb153_cadj_Log2): Has a distribution with right skewness, suggesting that exposure to these compounds is higher among a smaller segment of the population.

PCB 170 (hs_pcb170_cadj_Log2): This histograms show a significant right skew, indicating lower concentrations of these chemicals in most samples, with fewer samples showing higher concentrations. This pattern suggests that while most individuals have low exposure, a few may have considerably higher levels.

DEP and PBDE 153: These histograms mostly show multimodal distributions (more than one peak), suggesting different exposure sources or groups within the population that have distinct exposure levels. The multiple peaks could indicate varied exposure pathways or differences in how these chemicals are metabolized or retained in the body.

PFHxS and PFOA: These perfluorinated compounds display a roughly normal distribution skewed right, suggesting a common source of exposure among the population, but with some individuals experiencing higher exposures.

PFOS and PFUnDA: The histograms show a single, sharp peak with a rapid decline, indicating that most individuals have similar exposure levels, likely due to common environmental sources or regulatory controls limiting variability.

MBZP (Monobenzyl Phthalate): This histogram shows a right-skewed distribution. Most values cluster at the lower end, indicating a common lower exposure level among subjects, with a long tail towards higher values suggesting occasional higher exposures.

MECPP (Mono-ethyl hexyl phthalate): The distribution is right-skewed, similar to MBZP, but with a smoother decline. This pattern also indicates that while most subjects have lower exposure levels, a few experience significantly higher exposures.

MEHHP (Mono-2-ethyl-5-hydroxyhexyl phthalate): Exhibits a unimodal distribution with a peak around a middle value and symmetric tails. This could indicate a more standardized exposure level among the subjects with some variation.

MEHP (Mono-ethylhexyl phthalate):Another right-skewed distribution, indicating that most subjects have lower exposure levels but a few have much higher levels.

MEOHP (Mono-2-ethyl-5-oxohexyl phthalate): This histogram shows a distribution with a peak around the middle values and a tail extending towards higher values, suggesting a central tendency with some higher exposures.

MEP (Mono-ethyl phthalate): The distribution is right-skewed, similar to others, showing most subjects with low to moderate levels of exposure, but a few have much higher levels.

numeric_chemical <- select_if(chemical_exposome, is.numeric)
cor_matrix <- cor(numeric_chemical, method = "pearson")
cor_matrix <- cor(numeric_chemical, method = "spearman")
custom_color_scale <- list(
  c(0, "darkred"),    
  c(0.5, "white"), 
  c(1, "darkblue")
)

plot_ly(
  z = cor_matrix, 
  x = colnames(cor_matrix), 
  y = colnames(cor_matrix), 
  type = "heatmap",
  colorscale = custom_color_scale
) %>%
layout(
  title = "Correlation Matrix",
  xaxis = list(tickangle = -90),
  yaxis = list(side = "left")
)

Data Summary Covariates

# Specified covariates
specific_covariates <- c(
  "e3_sex_None", 
  "e3_yearbir_None", 
  "h_edumc_None", 
  "h_cohort", 
  "hs_child_age_None"
)

covariate_data <- dplyr::select(covariates, all_of(specific_covariates))
summarytools::view(dfSummary(covariate_data, style = 'grid', plain.ascii = FALSE, valid.col = FALSE, headings = FALSE), method = "render")
No Variable Stats / Values Freqs (% of Valid) Graph Missing
1 e3_sex_None [factor]
1. female
2. male
608(46.7%)
693(53.3%)
 0 (0.0%)
2 e3_yearbir_None [factor]
1. 2003
2. 2004
3. 2005
4. 2006
5. 2007
6. 2008
7. 2009
55(4.2%)
107(8.2%)
241(18.5%)
256(19.7%)
250(19.2%)
379(29.1%)
13(1.0%)
 0 (0.0%)
3 h_edumc_None [factor]
1. 1
2. 2
3. 3
178(13.7%)
449(34.5%)
674(51.8%)
 0 (0.0%)
4 h_cohort [factor]
1. 1
2. 2
3. 3
4. 4
5. 5
6. 6
202(15.5%)
198(15.2%)
224(17.2%)
207(15.9%)
272(20.9%)
198(15.2%)
 0 (0.0%)
5 hs_child_age_None [numeric]
Mean (sd) : 8 (1.6)
min ≤ med ≤ max:
5.4 ≤ 8 ≤ 12.1
IQR (CV) : 2.4 (0.2)
 879 distinct values 0 (0.0%)

Generated by summarytools 1.0.1 (R version 4.4.0)
2024-07-09

#separate numeric and categorical data
numeric_covariates <- covariate_data %>% 
  dplyr::select(where(is.numeric))

numeric_covariates_long <- pivot_longer(
  numeric_covariates,
  cols = everything(),
  names_to = "variable",
  values_to = "value"
)

unique_numerical_vars <- unique(numeric_covariates_long$variable)

num_plots <- lapply(unique_numerical_vars, function(var) {
  data <- filter(numeric_covariates_long, variable == var)
  p <- ggplot(data, aes(x = value)) +
    geom_histogram(bins = 30, fill = "blue") +
    labs(title = paste("Histogram of", var), x = "Value", y = "Count")
  print(p)
  return(p)
})

Child’s Age (hs_child_age): This histogram is multimodal, reflecting several peaks across different ages. This could be indicative of the data collection points or particular age groups being studied.

categorical_covariates <- covariate_data %>% 
  dplyr::select(where(is.factor))

categorical_covariates_long <- pivot_longer(
  categorical_covariates,
  cols = everything(),
  names_to = "variable",
  values_to = "value"
)

unique_categorical_vars <- unique(categorical_covariates_long$variable)
categorical_plots <- lapply(unique_categorical_vars, function(var) {
  data <- filter(categorical_covariates_long, variable == var)
  
  p <- ggplot(data, aes(x = value, fill = value)) +
    geom_bar(stat = "count") +
    labs(title = paste("Distribution of", var), x = var, y = "Count")
  
  print(p)
  return(p)
})

Cohorts (h_cohort): The distribution shows the count of subjects across six different cohorts. All cohorts have a substantial number of subjects, with cohort 5 showing the highest participation.

Gender Distribution (e3_sex): The gender distribution is nearly balanced with a slight higher count for males compared to females.

Year of Birth (e3_yearbir): This chart shows that the majority of subjects were born in the later years, with a significant increase in 2009, indicating perhaps a larger recruitment or a specific cohort focus that year.

Educational Level (h_educmc): Represents three categories of educational attainment, with category 3 having the highest count, suggesting a higher level of education among the majority of the subjects.

Data Summary Outcome: Phenotype

outcome_BMI <- phenotype %>% 
  dplyr::select(hs_zbmi_who)
summarytools::view(dfSummary(outcome_BMI, style = 'grid', plain.ascii = FALSE, valid.col = FALSE, headings = FALSE), method = "render")
No Variable Stats / Values Freqs (% of Valid) Graph Missing
1 hs_zbmi_who [numeric]
Mean (sd) : 0.4 (1.2)
min ≤ med ≤ max:
-3.6 ≤ 0.3 ≤ 4.7
IQR (CV) : 1.5 (3)
 421 distinct values 0 (0.0%)

Generated by summarytools 1.0.1 (R version 4.4.0)
2024-07-09

# Combine all selected data
combined_data <- cbind(covariate_data, lifestyle_exposome, chemical_exposome, outcome_BMI)

# Ensure no duplicated columns
combined_data <- combined_data[, !duplicated(colnames(combined_data))]

# Convert sex variable to a factor for stratification
combined_data$e3_sex_None <- as.factor(combined_data$e3_sex_None)
levels(combined_data$e3_sex_None) <- c("Male", "Female")

render_cont <- function(x) {
  with(stats.default(x), sprintf("%0.2f (%0.2f)", MEAN, SD))
}

render_cat <- function(x) {
  c("", sapply(stats.default(x), function(y) with(y, sprintf("%d (%0.1f %%)", FREQ, PCT))))
}

# Define the formula for table1
table1_formula <- ~ 
  hs_child_age_None + e3_yearbir_None + h_edumc_None + h_cohort +
  hs_zbmi_who +
  h_bfdur_Ter + hs_bakery_prod_Ter + hs_break_cer_Ter + hs_dairy_Ter + hs_fastfood_Ter + hs_org_food_Ter +
  hs_proc_meat_Ter +
  hs_total_fish_Ter + hs_total_fruits_Ter + hs_total_lipids_Ter + hs_total_sweets_Ter + hs_total_veg_Ter +
  hs_cd_c_Log2 + hs_co_c_Log2 + hs_cs_c_Log2 + hs_cu_c_Log2 +
  hs_hg_c_Log2 + hs_mo_c_Log2 + hs_dde_cadj_Log2 + hs_pcb153_cadj_Log2 +
  hs_pcb170_cadj_Log2 + hs_dep_cadj_Log2 + hs_pbde153_cadj_Log2 +
  hs_pfhxs_c_Log2 + hs_pfoa_c_Log2 + hs_pfos_c_Log2 + hs_prpa_cadj_Log2 +
  hs_mbzp_cadj_Log2 + hs_mibp_cadj_Log2 + hs_mnbp_cadj_Log2 | e3_sex_None

# Create the table
table1(
  table1_formula,
  data = combined_data,
  render.continuous = render_cont,
  render.categorical = render_cat,
  overall = TRUE,
  topclass = "Rtable1-shade"
)
Male
(N=608)		 Female
(N=693)		 TRUE
(N=1301)
hs_child_age_None 7.91 (1.58) 8.03 (1.64) 7.98 (1.61)
e3_yearbir_None
2003 25 (4.1 %) 30 (4.3 %) 55 (4.2 %)
2004 46 (7.6 %) 61 (8.8 %) 107 (8.2 %)
2005 121 (19.9 %) 120 (17.3 %) 241 (18.5 %)
2006 108 (17.8 %) 148 (21.4 %) 256 (19.7 %)
2007 128 (21.1 %) 122 (17.6 %) 250 (19.2 %)
2008 177 (29.1 %) 202 (29.1 %) 379 (29.1 %)
2009 3 (0.5 %) 10 (1.4 %) 13 (1.0 %)
h_edumc_None
1 96 (15.8 %) 82 (11.8 %) 178 (13.7 %)
2 195 (32.1 %) 254 (36.7 %) 449 (34.5 %)
3 317 (52.1 %) 357 (51.5 %) 674 (51.8 %)
h_cohort
1 97 (16.0 %) 105 (15.2 %) 202 (15.5 %)
2 86 (14.1 %) 112 (16.2 %) 198 (15.2 %)
3 102 (16.8 %) 122 (17.6 %) 224 (17.2 %)
4 93 (15.3 %) 114 (16.5 %) 207 (15.9 %)
5 129 (21.2 %) 143 (20.6 %) 272 (20.9 %)
6 101 (16.6 %) 97 (14.0 %) 198 (15.2 %)
hs_zbmi_who 0.35 (1.15) 0.45 (1.22) 0.40 (1.19)
h_bfdur_Ter
(0,10.8] 231 (38.0 %) 275 (39.7 %) 506 (38.9 %)
(10.8,34.9] 118 (19.4 %) 152 (21.9 %) 270 (20.8 %)
(34.9,Inf] 259 (42.6 %) 266 (38.4 %) 525 (40.4 %)
hs_bakery_prod_Ter
(0,2] 164 (27.0 %) 181 (26.1 %) 345 (26.5 %)
(2,6] 188 (30.9 %) 235 (33.9 %) 423 (32.5 %)
(6,Inf] 256 (42.1 %) 277 (40.0 %) 533 (41.0 %)
hs_break_cer_Ter
(0,1.1] 141 (23.2 %) 150 (21.6 %) 291 (22.4 %)
(1.1,5.5] 251 (41.3 %) 270 (39.0 %) 521 (40.0 %)
(5.5,Inf] 216 (35.5 %) 273 (39.4 %) 489 (37.6 %)
hs_dairy_Ter
(0,14.6] 175 (28.8 %) 184 (26.6 %) 359 (27.6 %)
(14.6,25.6] 229 (37.7 %) 236 (34.1 %) 465 (35.7 %)
(25.6,Inf] 204 (33.6 %) 273 (39.4 %) 477 (36.7 %)
hs_fastfood_Ter
(0,0.132] 75 (12.3 %) 68 (9.8 %) 143 (11.0 %)
(0.132,0.5] 273 (44.9 %) 330 (47.6 %) 603 (46.3 %)
(0.5,Inf] 260 (42.8 %) 295 (42.6 %) 555 (42.7 %)
hs_org_food_Ter
(0,0.132] 211 (34.7 %) 218 (31.5 %) 429 (33.0 %)
(0.132,1] 191 (31.4 %) 205 (29.6 %) 396 (30.4 %)
(1,Inf] 206 (33.9 %) 270 (39.0 %) 476 (36.6 %)
hs_proc_meat_Ter
(0,1.5] 175 (28.8 %) 191 (27.6 %) 366 (28.1 %)
(1.5,4] 227 (37.3 %) 244 (35.2 %) 471 (36.2 %)
(4,Inf] 206 (33.9 %) 258 (37.2 %) 464 (35.7 %)
hs_total_fish_Ter
(0,1.5] 183 (30.1 %) 206 (29.7 %) 389 (29.9 %)
(1.5,3] 224 (36.8 %) 230 (33.2 %) 454 (34.9 %)
(3,Inf] 201 (33.1 %) 257 (37.1 %) 458 (35.2 %)
hs_total_fruits_Ter
(0,7] 174 (28.6 %) 239 (34.5 %) 413 (31.7 %)
(7,14.1] 216 (35.5 %) 191 (27.6 %) 407 (31.3 %)
(14.1,Inf] 218 (35.9 %) 263 (38.0 %) 481 (37.0 %)
hs_total_lipids_Ter
(0,3] 193 (31.7 %) 204 (29.4 %) 397 (30.5 %)
(3,7] 171 (28.1 %) 232 (33.5 %) 403 (31.0 %)
(7,Inf] 244 (40.1 %) 257 (37.1 %) 501 (38.5 %)
hs_total_sweets_Ter
(0,4.1] 149 (24.5 %) 195 (28.1 %) 344 (26.4 %)
(4.1,8.5] 251 (41.3 %) 265 (38.2 %) 516 (39.7 %)
(8.5,Inf] 208 (34.2 %) 233 (33.6 %) 441 (33.9 %)
hs_total_veg_Ter
(0,6] 190 (31.2 %) 214 (30.9 %) 404 (31.1 %)
(6,8.5] 136 (22.4 %) 178 (25.7 %) 314 (24.1 %)
(8.5,Inf] 282 (46.4 %) 301 (43.4 %) 583 (44.8 %)
hs_cd_c_Log2 -3.99 (0.98) -3.95 (1.09) -3.97 (1.04)
hs_co_c_Log2 -2.37 (0.61) -2.32 (0.64) -2.34 (0.63)
hs_cs_c_Log2 0.44 (0.58) 0.44 (0.57) 0.44 (0.57)
hs_cu_c_Log2 9.81 (0.25) 9.84 (0.22) 9.83 (0.23)
hs_hg_c_Log2 -0.24 (1.59) -0.35 (1.75) -0.30 (1.68)
hs_mo_c_Log2 -0.32 (0.83) -0.31 (0.96) -0.32 (0.90)
hs_dde_cadj_Log2 4.63 (1.48) 4.70 (1.50) 4.67 (1.49)
hs_pcb153_cadj_Log2 3.47 (0.86) 3.63 (0.94) 3.56 (0.90)
hs_pcb170_cadj_Log2 -0.60 (3.22) -0.05 (2.77) -0.31 (3.00)
hs_dep_cadj_Log2 0.27 (3.16) 0.06 (3.25) 0.16 (3.21)
hs_pbde153_cadj_Log2 -4.66 (3.86) -4.40 (3.80) -4.53 (3.83)
hs_pfhxs_c_Log2 -1.62 (1.30) -1.53 (1.31) -1.57 (1.31)
hs_pfoa_c_Log2 0.60 (0.55) 0.62 (0.56) 0.61 (0.55)
hs_pfos_c_Log2 0.95 (1.15) 0.99 (1.08) 0.97 (1.11)
hs_prpa_cadj_Log2 -1.26 (3.96) -1.91 (3.68) -1.61 (3.82)
hs_mbzp_cadj_Log2 2.42 (1.23) 2.47 (1.22) 2.44 (1.22)
hs_mibp_cadj_Log2 5.54 (1.09) 5.39 (1.12) 5.46 (1.11)
hs_mnbp_cadj_Log2 4.77 (1.08) 4.60 (0.96) 4.68 (1.02) 
combined_data$h_cohort <- as.factor(combined_data$h_cohort)
# Create the table
table1(
  ~ hs_child_age_None + e3_sex_None + e3_yearbir_None + h_edumc_None +
    hs_zbmi_who + h_bfdur_Ter + hs_bakery_prod_Ter +
    hs_break_cer_Ter + hs_dairy_Ter + hs_fastfood_Ter +
    hs_org_food_Ter + hs_proc_meat_Ter + hs_total_fish_Ter + hs_total_fruits_Ter +
    hs_total_lipids_Ter +
    hs_total_sweets_Ter + hs_total_veg_Ter +
    hs_cd_c_Log2 + hs_co_c_Log2 + hs_cs_c_Log2 + hs_cu_c_Log2 +
    hs_hg_c_Log2 + hs_mo_c_Log2 + hs_dde_cadj_Log2 + hs_pcb153_cadj_Log2 +
    hs_pcb170_cadj_Log2 + hs_dep_cadj_Log2 + hs_pbde153_cadj_Log2 +
    hs_pfhxs_c_Log2 + hs_pfoa_c_Log2 + hs_pfos_c_Log2 + hs_prpa_cadj_Log2 +
    hs_mbzp_cadj_Log2 + hs_mibp_cadj_Log2 + hs_mnbp_cadj_Log2 | h_cohort,
    data = combined_data,
  render.continuous = render_cont,
  render.categorical = render_cat,
  overall = TRUE,
  topclass = "Rtable1-shade"
)
1
(N=202)		 2
(N=198)		 3
(N=224)		 4
(N=207)		 5
(N=272)		 6
(N=198)		 TRUE
(N=1301)
hs_child_age_None 6.61 (0.28) 10.82 (0.58) 8.78 (0.58) 6.48 (0.47) 8.46 (0.53) 6.51 (0.30) 7.98 (1.61)
e3_sex_None
Male 97 (48.0 %) 86 (43.4 %) 102 (45.5 %) 93 (44.9 %) 129 (47.4 %) 101 (51.0 %) 608 (46.7 %)
Female 105 (52.0 %) 112 (56.6 %) 122 (54.5 %) 114 (55.1 %) 143 (52.6 %) 97 (49.0 %) 693 (53.3 %)
e3_yearbir_None
2003 0 (0.0 %) 55 (27.8 %) 0 (0.0 %) 0 (0.0 %) 0 (0.0 %) 0 (0.0 %) 55 (4.2 %)
2004 0 (0.0 %) 107 (54.0 %) 0 (0.0 %) 0 (0.0 %) 0 (0.0 %) 0 (0.0 %) 107 (8.2 %)
2005 0 (0.0 %) 36 (18.2 %) 120 (53.6 %) 0 (0.0 %) 85 (31.2 %) 0 (0.0 %) 241 (18.5 %)
2006 0 (0.0 %) 0 (0.0 %) 99 (44.2 %) 0 (0.0 %) 157 (57.7 %) 0 (0.0 %) 256 (19.7 %)
2007 82 (40.6 %) 0 (0.0 %) 5 (2.2 %) 62 (30.0 %) 30 (11.0 %) 71 (35.9 %) 250 (19.2 %)
2008 117 (57.9 %) 0 (0.0 %) 0 (0.0 %) 136 (65.7 %) 0 (0.0 %) 126 (63.6 %) 379 (29.1 %)
2009 3 (1.5 %) 0 (0.0 %) 0 (0.0 %) 9 (4.3 %) 0 (0.0 %) 1 (0.5 %) 13 (1.0 %)
h_edumc_None
1 90 (44.6 %) 14 (7.1 %) 56 (25.0 %) 9 (4.3 %) 0 (0.0 %) 9 (4.5 %) 178 (13.7 %)
2 42 (20.8 %) 72 (36.4 %) 91 (40.6 %) 70 (33.8 %) 60 (22.1 %) 114 (57.6 %) 449 (34.5 %)
3 70 (34.7 %) 112 (56.6 %) 77 (34.4 %) 128 (61.8 %) 212 (77.9 %) 75 (37.9 %) 674 (51.8 %)
hs_zbmi_who 0.20 (1.15) 0.19 (1.13) 0.80 (1.22) 0.52 (1.22) 0.09 (0.90) 0.68 (1.37) 0.40 (1.19)
h_bfdur_Ter
(0,10.8] 74 (36.6 %) 119 (60.1 %) 70 (31.2 %) 58 (28.0 %) 101 (37.1 %) 84 (42.4 %) 506 (38.9 %)
(10.8,34.9] 2 (1.0 %) 57 (28.8 %) 100 (44.6 %) 30 (14.5 %) 0 (0.0 %) 81 (40.9 %) 270 (20.8 %)
(34.9,Inf] 126 (62.4 %) 22 (11.1 %) 54 (24.1 %) 119 (57.5 %) 171 (62.9 %) 33 (16.7 %) 525 (40.4 %)
hs_bakery_prod_Ter
(0,2] 29 (14.4 %) 41 (20.7 %) 39 (17.4 %) 34 (16.4 %) 187 (68.8 %) 15 (7.6 %) 345 (26.5 %)
(2,6] 66 (32.7 %) 51 (25.8 %) 89 (39.7 %) 84 (40.6 %) 74 (27.2 %) 59 (29.8 %) 423 (32.5 %)
(6,Inf] 107 (53.0 %) 106 (53.5 %) 96 (42.9 %) 89 (43.0 %) 11 (4.0 %) 124 (62.6 %) 533 (41.0 %)
hs_break_cer_Ter
(0,1.1] 18 (8.9 %) 65 (32.8 %) 61 (27.2 %) 38 (18.4 %) 57 (21.0 %) 52 (26.3 %) 291 (22.4 %)
(1.1,5.5] 55 (27.2 %) 67 (33.8 %) 89 (39.7 %) 101 (48.8 %) 114 (41.9 %) 95 (48.0 %) 521 (40.0 %)
(5.5,Inf] 129 (63.9 %) 66 (33.3 %) 74 (33.0 %) 68 (32.9 %) 101 (37.1 %) 51 (25.8 %) 489 (37.6 %)
hs_dairy_Ter
(0,14.6] 21 (10.4 %) 41 (20.7 %) 55 (24.6 %) 128 (61.8 %) 76 (27.9 %) 38 (19.2 %) 359 (27.6 %)
(14.6,25.6] 86 (42.6 %) 49 (24.7 %) 99 (44.2 %) 51 (24.6 %) 91 (33.5 %) 89 (44.9 %) 465 (35.7 %)
(25.6,Inf] 95 (47.0 %) 108 (54.5 %) 70 (31.2 %) 28 (13.5 %) 105 (38.6 %) 71 (35.9 %) 477 (36.7 %)
hs_fastfood_Ter
(0,0.132] 18 (8.9 %) 23 (11.6 %) 18 (8.0 %) 51 (24.6 %) 24 (8.8 %) 9 (4.5 %) 143 (11.0 %)
(0.132,0.5] 40 (19.8 %) 101 (51.0 %) 127 (56.7 %) 106 (51.2 %) 169 (62.1 %) 60 (30.3 %) 603 (46.3 %)
(0.5,Inf] 144 (71.3 %) 74 (37.4 %) 79 (35.3 %) 50 (24.2 %) 79 (29.0 %) 129 (65.2 %) 555 (42.7 %)
hs_org_food_Ter
(0,0.132] 114 (56.4 %) 51 (25.8 %) 118 (52.7 %) 19 (9.2 %) 9 (3.3 %) 118 (59.6 %) 429 (33.0 %)
(0.132,1] 40 (19.8 %) 73 (36.9 %) 70 (31.2 %) 75 (36.2 %) 109 (40.1 %) 29 (14.6 %) 396 (30.4 %)
(1,Inf] 48 (23.8 %) 74 (37.4 %) 36 (16.1 %) 113 (54.6 %) 154 (56.6 %) 51 (25.8 %) 476 (36.6 %)
hs_proc_meat_Ter
(0,1.5] 118 (58.4 %) 47 (23.7 %) 25 (11.2 %) 83 (40.1 %) 39 (14.3 %) 54 (27.3 %) 366 (28.1 %)
(1.5,4] 32 (15.8 %) 90 (45.5 %) 85 (37.9 %) 71 (34.3 %) 85 (31.2 %) 108 (54.5 %) 471 (36.2 %)
(4,Inf] 52 (25.7 %) 61 (30.8 %) 114 (50.9 %) 53 (25.6 %) 148 (54.4 %) 36 (18.2 %) 464 (35.7 %)
hs_total_fish_Ter
(0,1.5] 82 (40.6 %) 38 (19.2 %) 25 (11.2 %) 130 (62.8 %) 38 (14.0 %) 76 (38.4 %) 389 (29.9 %)
(1.5,3] 53 (26.2 %) 103 (52.0 %) 47 (21.0 %) 57 (27.5 %) 94 (34.6 %) 100 (50.5 %) 454 (34.9 %)
(3,Inf] 67 (33.2 %) 57 (28.8 %) 152 (67.9 %) 20 (9.7 %) 140 (51.5 %) 22 (11.1 %) 458 (35.2 %)
hs_total_fruits_Ter
(0,7] 26 (12.9 %) 107 (54.0 %) 83 (37.1 %) 99 (47.8 %) 35 (12.9 %) 63 (31.8 %) 413 (31.7 %)
(7,14.1] 42 (20.8 %) 45 (22.7 %) 85 (37.9 %) 64 (30.9 %) 82 (30.1 %) 89 (44.9 %) 407 (31.3 %)
(14.1,Inf] 134 (66.3 %) 46 (23.2 %) 56 (25.0 %) 44 (21.3 %) 155 (57.0 %) 46 (23.2 %) 481 (37.0 %)
hs_total_lipids_Ter
(0,3] 18 (8.9 %) 31 (15.7 %) 151 (67.4 %) 24 (11.6 %) 32 (11.8 %) 141 (71.2 %) 397 (30.5 %)
(3,7] 72 (35.6 %) 90 (45.5 %) 40 (17.9 %) 74 (35.7 %) 82 (30.1 %) 45 (22.7 %) 403 (31.0 %)
(7,Inf] 112 (55.4 %) 77 (38.9 %) 33 (14.7 %) 109 (52.7 %) 158 (58.1 %) 12 (6.1 %) 501 (38.5 %)
hs_total_sweets_Ter
(0,4.1] 50 (24.8 %) 39 (19.7 %) 93 (41.5 %) 19 (9.2 %) 89 (32.7 %) 54 (27.3 %) 344 (26.4 %)
(4.1,8.5] 77 (38.1 %) 61 (30.8 %) 88 (39.3 %) 58 (28.0 %) 125 (46.0 %) 107 (54.0 %) 516 (39.7 %)
(8.5,Inf] 75 (37.1 %) 98 (49.5 %) 43 (19.2 %) 130 (62.8 %) 58 (21.3 %) 37 (18.7 %) 441 (33.9 %)
hs_total_veg_Ter
(0,6] 65 (32.2 %) 53 (26.8 %) 94 (42.0 %) 81 (39.1 %) 42 (15.4 %) 69 (34.8 %) 404 (31.1 %)
(6,8.5] 41 (20.3 %) 42 (21.2 %) 69 (30.8 %) 53 (25.6 %) 57 (21.0 %) 52 (26.3 %) 314 (24.1 %)
(8.5,Inf] 96 (47.5 %) 103 (52.0 %) 61 (27.2 %) 73 (35.3 %) 173 (63.6 %) 77 (38.9 %) 583 (44.8 %)
hs_cd_c_Log2 -3.87 (0.84) -4.06 (1.22) -4.22 (1.23) -4.16 (1.11) -3.60 (0.74) -3.99 (0.91) -3.97 (1.04)
hs_co_c_Log2 -2.31 (0.52) -2.38 (0.56) -2.46 (0.64) -2.37 (0.64) -2.53 (0.64) -1.93 (0.56) -2.34 (0.63)
hs_cs_c_Log2 0.12 (0.45) 1.01 (0.47) 0.61 (0.45) -0.17 (0.39) 0.71 (0.40) 0.29 (0.39) 0.44 (0.57)
hs_cu_c_Log2 9.86 (0.23) 9.88 (0.25) 9.83 (0.20) 9.80 (0.21) 9.71 (0.21) 9.93 (0.21) 9.83 (0.23)
hs_hg_c_Log2 -0.56 (1.59) 0.67 (1.29) 0.92 (1.30) -1.97 (1.49) -0.34 (1.06) -0.57 (1.69) -0.30 (1.68)
hs_mo_c_Log2 -0.13 (0.79) -0.58 (1.18) -0.55 (0.77) -0.42 (0.84) -0.17 (0.74) -0.07 (0.95) -0.32 (0.90)
hs_dde_cadj_Log2 3.81 (1.31) 4.01 (1.28) 4.36 (1.24) 5.67 (1.29) 4.26 (0.94) 6.06 (1.41) 4.67 (1.49)
hs_pcb153_cadj_Log2 2.73 (0.63) 3.50 (0.76) 3.66 (0.84) 3.93 (0.85) 4.22 (0.69) 3.03 (0.68) 3.56 (0.90)
hs_pcb170_cadj_Log2 -2.44 (3.33) 0.33 (1.89) 0.41 (2.42) -0.81 (3.58) 1.38 (1.63) -1.38 (3.14) -0.31 (3.00)
hs_dep_cadj_Log2 1.44 (3.30) -0.27 (3.31) -0.15 (3.07) -1.42 (3.25) 0.62 (2.85) 0.66 (2.82) 0.16 (3.21)
hs_pbde153_cadj_Log2 -3.39 (3.79) -5.11 (3.61) -5.05 (3.83) -4.86 (3.78) -2.66 (3.00) -6.71 (3.67) -4.53 (3.83)
hs_pfhxs_c_Log2 -1.48 (1.03) -0.51 (0.83) -1.55 (0.88) -2.69 (1.19) -0.66 (0.76) -2.83 (1.08) -1.57 (1.31)
hs_pfoa_c_Log2 0.86 (0.50) 0.56 (0.53) 0.52 (0.51) 0.42 (0.61) 0.80 (0.43) 0.46 (0.61) 0.61 (0.55)
hs_pfos_c_Log2 0.57 (0.90) 1.64 (0.78) 0.43 (0.97) 0.19 (1.29) 1.67 (0.75) 1.16 (0.88) 0.97 (1.11)
hs_prpa_cadj_Log2 -0.05 (3.69) -2.65 (3.49) 0.69 (3.83) -2.00 (3.98) -3.14 (2.92) -2.22 (3.50) -1.61 (3.82)
hs_mbzp_cadj_Log2 1.60 (1.16) 2.81 (1.19) 2.52 (1.09) 2.81 (1.11) 2.17 (1.11) 2.85 (1.23) 2.44 (1.22)
hs_mibp_cadj_Log2 6.07 (1.02) 5.47 (1.07) 4.88 (0.90) 6.27 (0.87) 4.74 (0.99) 5.63 (0.83) 5.46 (1.11)
hs_mnbp_cadj_Log2 4.74 (0.90) 4.24 (0.86) 3.99 (0.79) 5.47 (0.86) 4.79 (0.89) 4.84 (1.12) 4.68 (1.02) 
combined_data$h_edumc_None <- as.factor(combined_data$h_edumc_None)
table1(
  ~ hs_child_age_None + e3_sex_None + e3_yearbir_None + hs_zbmi_who +
    h_bfdur_Ter + hs_bakery_prod_Ter + hs_break_cer_Ter + hs_dairy_Ter + hs_fastfood_Ter + hs_org_food_Ter +
    hs_proc_meat_Ter +
    hs_total_fish_Ter + hs_total_fruits_Ter + hs_total_lipids_Ter + hs_total_sweets_Ter + 
    hs_total_veg_Ter + hs_cd_c_Log2 + hs_co_c_Log2 + 
    hs_cs_c_Log2 + hs_cu_c_Log2 + hs_hg_c_Log2 + hs_mo_c_Log2 + hs_dde_cadj_Log2 +
    hs_pcb153_cadj_Log2 + hs_pcb170_cadj_Log2 + hs_dep_cadj_Log2 +
    hs_pbde153_cadj_Log2 + hs_pfhxs_c_Log2 + hs_pfoa_c_Log2 + hs_pfos_c_Log2 + 
    hs_prpa_cadj_Log2 + hs_mbzp_cadj_Log2 + hs_mibp_cadj_Log2 + hs_mnbp_cadj_Log2 | h_edumc_None,
  data = combined_data,
  render.continuous = render_cont,
  render.categorical = render_cat,
  overall = TRUE,
  topclass = "Rtable1-shade"
)
1
(N=178)		 2
(N=449)		 3
(N=674)		 TRUE
(N=1301)
hs_child_age_None 7.61 (1.43) 7.97 (1.68) 8.07 (1.60) 7.98 (1.61)
e3_sex_None
Male 96 (53.9 %) 195 (43.4 %) 317 (47.0 %) 608 (46.7 %)
Female 82 (46.1 %) 254 (56.6 %) 357 (53.0 %) 693 (53.3 %)
e3_yearbir_None
2003 5 (2.8 %) 20 (4.5 %) 30 (4.5 %) 55 (4.2 %)
2004 6 (3.4 %) 43 (9.6 %) 58 (8.6 %) 107 (8.2 %)
2005 33 (18.5 %) 84 (18.7 %) 124 (18.4 %) 241 (18.5 %)
2006 25 (14.0 %) 73 (16.3 %) 158 (23.4 %) 256 (19.7 %)
2007 42 (23.6 %) 89 (19.8 %) 119 (17.7 %) 250 (19.2 %)
2008 65 (36.5 %) 136 (30.3 %) 178 (26.4 %) 379 (29.1 %)
2009 2 (1.1 %) 4 (0.9 %) 7 (1.0 %) 13 (1.0 %)
hs_zbmi_who 0.39 (1.27) 0.57 (1.26) 0.30 (1.11) 0.40 (1.19)
h_bfdur_Ter
(0,10.8] 69 (38.8 %) 200 (44.5 %) 237 (35.2 %) 506 (38.9 %)
(10.8,34.9] 31 (17.4 %) 111 (24.7 %) 128 (19.0 %) 270 (20.8 %)
(34.9,Inf] 78 (43.8 %) 138 (30.7 %) 309 (45.8 %) 525 (40.4 %)
hs_bakery_prod_Ter
(0,2] 28 (15.7 %) 105 (23.4 %) 212 (31.5 %) 345 (26.5 %)
(2,6] 58 (32.6 %) 151 (33.6 %) 214 (31.8 %) 423 (32.5 %)
(6,Inf] 92 (51.7 %) 193 (43.0 %) 248 (36.8 %) 533 (41.0 %)
hs_break_cer_Ter
(0,1.1] 31 (17.4 %) 118 (26.3 %) 142 (21.1 %) 291 (22.4 %)
(1.1,5.5] 60 (33.7 %) 191 (42.5 %) 270 (40.1 %) 521 (40.0 %)
(5.5,Inf] 87 (48.9 %) 140 (31.2 %) 262 (38.9 %) 489 (37.6 %)
hs_dairy_Ter
(0,14.6] 29 (16.3 %) 122 (27.2 %) 208 (30.9 %) 359 (27.6 %)
(14.6,25.6] 79 (44.4 %) 163 (36.3 %) 223 (33.1 %) 465 (35.7 %)
(25.6,Inf] 70 (39.3 %) 164 (36.5 %) 243 (36.1 %) 477 (36.7 %)
hs_fastfood_Ter
(0,0.132] 19 (10.7 %) 36 (8.0 %) 88 (13.1 %) 143 (11.0 %)
(0.132,0.5] 62 (34.8 %) 204 (45.4 %) 337 (50.0 %) 603 (46.3 %)
(0.5,Inf] 97 (54.5 %) 209 (46.5 %) 249 (36.9 %) 555 (42.7 %)
hs_org_food_Ter
(0,0.132] 120 (67.4 %) 179 (39.9 %) 130 (19.3 %) 429 (33.0 %)
(0.132,1] 31 (17.4 %) 131 (29.2 %) 234 (34.7 %) 396 (30.4 %)
(1,Inf] 27 (15.2 %) 139 (31.0 %) 310 (46.0 %) 476 (36.6 %)
hs_proc_meat_Ter
(0,1.5] 68 (38.2 %) 121 (26.9 %) 177 (26.3 %) 366 (28.1 %)
(1.5,4] 48 (27.0 %) 184 (41.0 %) 239 (35.5 %) 471 (36.2 %)
(4,Inf] 62 (34.8 %) 144 (32.1 %) 258 (38.3 %) 464 (35.7 %)
hs_total_fish_Ter
(0,1.5] 55 (30.9 %) 152 (33.9 %) 182 (27.0 %) 389 (29.9 %)
(1.5,3] 52 (29.2 %) 163 (36.3 %) 239 (35.5 %) 454 (34.9 %)
(3,Inf] 71 (39.9 %) 134 (29.8 %) 253 (37.5 %) 458 (35.2 %)
hs_total_fruits_Ter
(0,7] 51 (28.7 %) 169 (37.6 %) 193 (28.6 %) 413 (31.7 %)
(7,14.1] 48 (27.0 %) 135 (30.1 %) 224 (33.2 %) 407 (31.3 %)
(14.1,Inf] 79 (44.4 %) 145 (32.3 %) 257 (38.1 %) 481 (37.0 %)
hs_total_lipids_Ter
(0,3] 53 (29.8 %) 156 (34.7 %) 188 (27.9 %) 397 (30.5 %)
(3,7] 49 (27.5 %) 127 (28.3 %) 227 (33.7 %) 403 (31.0 %)
(7,Inf] 76 (42.7 %) 166 (37.0 %) 259 (38.4 %) 501 (38.5 %)
hs_total_sweets_Ter
(0,4.1] 56 (31.5 %) 124 (27.6 %) 164 (24.3 %) 344 (26.4 %)
(4.1,8.5] 64 (36.0 %) 183 (40.8 %) 269 (39.9 %) 516 (39.7 %)
(8.5,Inf] 58 (32.6 %) 142 (31.6 %) 241 (35.8 %) 441 (33.9 %)
hs_total_veg_Ter
(0,6] 79 (44.4 %) 166 (37.0 %) 159 (23.6 %) 404 (31.1 %)
(6,8.5] 42 (23.6 %) 112 (24.9 %) 160 (23.7 %) 314 (24.1 %)
(8.5,Inf] 57 (32.0 %) 171 (38.1 %) 355 (52.7 %) 583 (44.8 %)
hs_cd_c_Log2 -4.01 (1.09) -3.99 (1.12) -3.94 (0.97) -3.97 (1.04)
hs_co_c_Log2 -2.40 (0.56) -2.28 (0.67) -2.37 (0.61) -2.34 (0.63)
hs_cs_c_Log2 0.30 (0.56) 0.43 (0.55) 0.49 (0.59) 0.44 (0.57)
hs_cu_c_Log2 9.84 (0.22) 9.85 (0.25) 9.81 (0.22) 9.83 (0.23)
hs_hg_c_Log2 -0.28 (1.82) -0.35 (1.74) -0.27 (1.59) -0.30 (1.68)
hs_mo_c_Log2 -0.37 (0.88) -0.27 (0.88) -0.33 (0.92) -0.32 (0.90)
hs_dde_cadj_Log2 3.90 (1.26) 4.71 (1.58) 4.85 (1.42) 4.67 (1.49)
hs_pcb153_cadj_Log2 2.95 (0.77) 3.32 (0.80) 3.87 (0.87) 3.56 (0.90)
hs_pcb170_cadj_Log2 -1.68 (3.44) -0.88 (3.15) 0.43 (2.53) -0.31 (3.00)
hs_dep_cadj_Log2 0.28 (3.41) 0.01 (3.21) 0.23 (3.15) 0.16 (3.21)
hs_pbde153_cadj_Log2 -4.19 (3.79) -5.13 (3.80) -4.21 (3.82) -4.53 (3.83)
hs_pfhxs_c_Log2 -1.65 (1.02) -1.85 (1.45) -1.36 (1.23) -1.57 (1.31)
hs_pfoa_c_Log2 0.58 (0.60) 0.50 (0.57) 0.69 (0.52) 0.61 (0.55)
hs_pfos_c_Log2 0.52 (0.99) 0.85 (1.15) 1.17 (1.07) 0.97 (1.11)
hs_prpa_cadj_Log2 -0.50 (3.66) -1.58 (4.04) -1.91 (3.67) -1.61 (3.82)
hs_mbzp_cadj_Log2 2.13 (1.22) 2.59 (1.27) 2.43 (1.18) 2.44 (1.22)
hs_mibp_cadj_Log2 5.71 (1.12) 5.52 (1.11) 5.36 (1.10) 5.46 (1.11)
hs_mnbp_cadj_Log2 4.53 (0.96) 4.64 (1.01) 4.74 (1.03) 4.68 (1.02)

All Interested Data

outcome_cov <- cbind(covariate_data, outcome_BMI)
outcome_cov <- outcome_cov[, !duplicated(colnames(outcome_cov))]
#the full chemicals list
chemicals_full <- c(
  "hs_as_c_Log2",
  "hs_cd_c_Log2",
  "hs_co_c_Log2",
  "hs_cs_c_Log2",
  "hs_cu_c_Log2",
  "hs_hg_c_Log2",
  "hs_mn_c_Log2",
  "hs_mo_c_Log2",
  "hs_pb_c_Log2",
  "hs_tl_cdich_None",
  "hs_dde_cadj_Log2",
  "hs_ddt_cadj_Log2",
  "hs_hcb_cadj_Log2",
  "hs_pcb118_cadj_Log2",
  "hs_pcb138_cadj_Log2",
  "hs_pcb153_cadj_Log2",
  "hs_pcb170_cadj_Log2",
  "hs_pcb180_cadj_Log2",
  "hs_dep_cadj_Log2",
  "hs_detp_cadj_Log2",
  "hs_dmdtp_cdich_None",
  "hs_dmp_cadj_Log2",
  "hs_dmtp_cadj_Log2",
  "hs_pbde153_cadj_Log2",
  "hs_pbde47_cadj_Log2",
  "hs_pfhxs_c_Log2",
  "hs_pfna_c_Log2",
  "hs_pfoa_c_Log2",
  "hs_pfos_c_Log2",
  "hs_pfunda_c_Log2",
  "hs_bpa_cadj_Log2",
  "hs_bupa_cadj_Log2",
  "hs_etpa_cadj_Log2",
  "hs_mepa_cadj_Log2",
  "hs_oxbe_cadj_Log2",
  "hs_prpa_cadj_Log2",
  "hs_trcs_cadj_Log2",
  "hs_mbzp_cadj_Log2",
  "hs_mecpp_cadj_Log2",
  "hs_mehhp_cadj_Log2",
  "hs_mehp_cadj_Log2",
  "hs_meohp_cadj_Log2",
  "hs_mep_cadj_Log2",
  "hs_mibp_cadj_Log2",
  "hs_mnbp_cadj_Log2",
  "hs_ohminp_cadj_Log2",
  "hs_oxominp_cadj_Log2",
  "hs_cotinine_cdich_None",
  "hs_globalexp2_None"
)

#postnatal diet for child
postnatal_diet <- c(
  "h_bfdur_Ter",
  "hs_bakery_prod_Ter",
  "hs_beverages_Ter",
  "hs_break_cer_Ter",
  "hs_caff_drink_Ter",
  "hs_dairy_Ter",
  "hs_fastfood_Ter",
  "hs_org_food_Ter",
  "hs_proc_meat_Ter",
  "hs_readymade_Ter",
  "hs_total_bread_Ter",
  "hs_total_cereal_Ter",
  "hs_total_fish_Ter",
  "hs_total_fruits_Ter",
  "hs_total_lipids_Ter",
  "hs_total_meat_Ter",
  "hs_total_potatoes_Ter",
  "hs_total_sweets_Ter",
  "hs_total_veg_Ter",
  "hs_total_yog_Ter"
)

chemicals_columns <- c(chemicals_full)
all_chemicals <- exposome %>% dplyr::select(all_of(chemicals_columns))

diet_columns <- c(postnatal_diet)
all_diet <- exposome %>% dplyr::select(all_of(diet_columns))

all_columns <- c(chemicals_full, postnatal_diet)
extracted_exposome <- exposome %>% dplyr::select(all_of(all_columns))

chemicals_outcome_cov <- cbind(outcome_cov, all_chemicals)

diet_outcome_cov <- cbind(outcome_cov, all_diet)

interested_data <- cbind(outcome_cov, extracted_exposome)
head(interested_data)
interested_data_corr <- select_if(interested_data, is.numeric)
cor_matrix <- cor(interested_data_corr, method = "pearson")
cor_matrix <- cor(interested_data_corr, method = "spearman")
custom_color_scale <- list(
  c(0, "darkred"),    
  c(0.5, "white"), 
  c(1, "darkblue")
)

plot_ly(
  z = cor_matrix, 
  x = colnames(cor_matrix), 
  y = colnames(cor_matrix), 
  type = "heatmap",
  colorscale = custom_color_scale
) %>%
layout(
  title = "Correlation Matrix",
  xaxis = list(tickangle = -90),
  yaxis = list(side = "left")
)

Comparing Models with and without Covariates

Chemicals Data

Predicting LASSO

#LASSO train/test 70-30
set.seed(101)
train_indices <- sample(seq_len(nrow(chemicals_outcome_cov)), size = floor(0.7 * nrow(interested_data)))
test_indices <- setdiff(seq_len(nrow(chemicals_outcome_cov)), train_indices)

x_train <- as.matrix(chemicals_outcome_cov[train_indices, setdiff(names(chemicals_outcome_cov), "hs_zbmi_who")])
y_train <- chemicals_outcome_cov$hs_zbmi_who[train_indices]

x_test <- as.matrix(chemicals_outcome_cov[test_indices, setdiff(names(chemicals_outcome_cov), "hs_zbmi_who")])
y_test <- chemicals_outcome_cov$hs_zbmi_who[test_indices]

x_train_chemicals_only <- as.matrix(chemicals_outcome_cov[train_indices, chemicals_full])
x_test_chemicals_only <- as.matrix(chemicals_outcome_cov[test_indices, chemicals_full])

fit_without_covariates_train <- cv.glmnet(x_train_chemicals_only, y_train, alpha = 1, family = "gaussian")
fit_without_covariates_test <- predict(fit_without_covariates_train, s = "lambda.min", newx = x_test_chemicals_only)
test_mse_without_covariates <- mean((y_test - fit_without_covariates_test)^2)

plot(fit_without_covariates_train, xvar = "lambda", main = "Coefficients Path (Without Covariates)")

best_lambda <- fit_without_covariates_train$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates_train, s = best_lambda)
## 50 x 1 sparse Matrix of class "dgCMatrix"
##                                   s1
## (Intercept)            -4.7797230131
## hs_as_c_Log2            .           
## hs_cd_c_Log2           -0.0238815730
## hs_co_c_Log2           -0.0011670319
## hs_cs_c_Log2            0.0771865955
## hs_cu_c_Log2            0.6071183261
## hs_hg_c_Log2           -0.0075730086
## hs_mn_c_Log2            .           
## hs_mo_c_Log2           -0.0992489424
## hs_pb_c_Log2           -0.0056257448
## hs_tl_cdich_None        .           
## hs_dde_cadj_Log2       -0.0378984008
## hs_ddt_cadj_Log2        .           
## hs_hcb_cadj_Log2        .           
## hs_pcb118_cadj_Log2     .           
## hs_pcb138_cadj_Log2     .           
## hs_pcb153_cadj_Log2    -0.1721262187
## hs_pcb170_cadj_Log2    -0.0557570999
## hs_pcb180_cadj_Log2     .           
## hs_dep_cadj_Log2       -0.0186165147
## hs_detp_cadj_Log2       .           
## hs_dmdtp_cdich_None     .           
## hs_dmp_cadj_Log2        .           
## hs_dmtp_cadj_Log2       .           
## hs_pbde153_cadj_Log2   -0.0357794002
## hs_pbde47_cadj_Log2     .           
## hs_pfhxs_c_Log2        -0.0019079468
## hs_pfna_c_Log2          .           
## hs_pfoa_c_Log2         -0.1360824261
## hs_pfos_c_Log2         -0.0478302901
## hs_pfunda_c_Log2        .           
## hs_bpa_cadj_Log2        .           
## hs_bupa_cadj_Log2       .           
## hs_etpa_cadj_Log2       .           
## hs_mepa_cadj_Log2       .           
## hs_oxbe_cadj_Log2       0.0008622765
## hs_prpa_cadj_Log2       0.0011728557
## hs_trcs_cadj_Log2       .           
## hs_mbzp_cadj_Log2       0.0373221816
## hs_mecpp_cadj_Log2      .           
## hs_mehhp_cadj_Log2      .           
## hs_mehp_cadj_Log2       .           
## hs_meohp_cadj_Log2      .           
## hs_mep_cadj_Log2        .           
## hs_mibp_cadj_Log2      -0.0477304169
## hs_mnbp_cadj_Log2      -0.0036235331
## hs_ohminp_cadj_Log2     .           
## hs_oxominp_cadj_Log2    .           
## hs_cotinine_cdich_None  .           
## hs_globalexp2_None      .
cat("Model without Covariates - Test MSE:", test_mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.231997

Predicting Ridge

# RIDGE
fit_without_covariates_train <- cv.glmnet(x_train_chemicals_only, y_train, alpha = 0, family = "gaussian")
fit_without_covariates_test <- predict(fit_without_covariates_train, s = "lambda.min", newx = x_test_chemicals_only)
test_mse_without_covariates <- mean((y_test - fit_without_covariates_test)^2)

plot(fit_without_covariates_train, xvar = "lambda", main = "Coefficients Path (Without Covariates)")

best_lambda <- fit_without_covariates_train$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates_train, s = best_lambda)
## 50 x 1 sparse Matrix of class "dgCMatrix"
##                                   s1
## (Intercept)            -4.469806e+00
## hs_as_c_Log2            6.590433e-03
## hs_cd_c_Log2           -4.093355e-02
## hs_co_c_Log2           -5.049922e-02
## hs_cs_c_Log2            1.230373e-01
## hs_cu_c_Log2            6.078479e-01
## hs_hg_c_Log2           -3.225520e-02
## hs_mn_c_Log2           -3.089195e-02
## hs_mo_c_Log2           -1.068154e-01
## hs_pb_c_Log2           -5.295956e-02
## hs_tl_cdich_None        .           
## hs_dde_cadj_Log2       -4.888006e-02
## hs_ddt_cadj_Log2        4.045085e-03
## hs_hcb_cadj_Log2       -1.857150e-02
## hs_pcb118_cadj_Log2     1.400112e-02
## hs_pcb138_cadj_Log2    -3.614513e-02
## hs_pcb153_cadj_Log2    -1.223407e-01
## hs_pcb170_cadj_Log2    -5.267521e-02
## hs_pcb180_cadj_Log2    -1.074695e-02
## hs_dep_cadj_Log2       -2.548881e-02
## hs_detp_cadj_Log2       8.051621e-03
## hs_dmdtp_cdich_None     .           
## hs_dmp_cadj_Log2       -2.097690e-03
## hs_dmtp_cadj_Log2       7.300567e-05
## hs_pbde153_cadj_Log2   -3.315313e-02
## hs_pbde47_cadj_Log2     5.273953e-03
## hs_pfhxs_c_Log2        -2.966308e-02
## hs_pfna_c_Log2          2.336166e-02
## hs_pfoa_c_Log2         -1.519872e-01
## hs_pfos_c_Log2         -6.495855e-02
## hs_pfunda_c_Log2        1.248503e-02
## hs_bpa_cadj_Log2        3.832688e-04
## hs_bupa_cadj_Log2       6.588467e-03
## hs_etpa_cadj_Log2      -6.098679e-03
## hs_mepa_cadj_Log2      -1.638466e-02
## hs_oxbe_cadj_Log2       1.390524e-02
## hs_prpa_cadj_Log2       1.258510e-02
## hs_trcs_cadj_Log2       2.878805e-03
## hs_mbzp_cadj_Log2       5.550048e-02
## hs_mecpp_cadj_Log2      1.627174e-03
## hs_mehhp_cadj_Log2      2.316991e-02
## hs_mehp_cadj_Log2      -1.662304e-02
## hs_meohp_cadj_Log2      1.137436e-02
## hs_mep_cadj_Log2        3.371106e-03
## hs_mibp_cadj_Log2      -5.391219e-02
## hs_mnbp_cadj_Log2      -4.383016e-02
## hs_ohminp_cadj_Log2    -2.886768e-02
## hs_oxominp_cadj_Log2    2.204660e-02
## hs_cotinine_cdich_None  .           
## hs_globalexp2_None      .
cat("Model without Covariates - Test MSE:", test_mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.188752

Predicting Elastic Net

# ELASTIC NET
fit_without_covariates_train <- cv.glmnet(x_train_chemicals_only, y_train, alpha = 0.5, family = "gaussian")
fit_without_covariates_test <- predict(fit_without_covariates_train, s = "lambda.min", newx = x_test_chemicals_only)
test_mse_without_covariates <- mean((y_test - fit_without_covariates_test)^2)

plot(fit_without_covariates_train, xvar = "lambda", main = "Coefficients Path (Without Covariates)")

best_lambda <- fit_without_covariates_train$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates_train, s = best_lambda)
## 50 x 1 sparse Matrix of class "dgCMatrix"
##                                  s1
## (Intercept)            -4.785950188
## hs_as_c_Log2            .          
## hs_cd_c_Log2           -0.025843356
## hs_co_c_Log2           -0.005835867
## hs_cs_c_Log2            0.084715330
## hs_cu_c_Log2            0.607379616
## hs_hg_c_Log2           -0.009800093
## hs_mn_c_Log2            .          
## hs_mo_c_Log2           -0.099724922
## hs_pb_c_Log2           -0.010318890
## hs_tl_cdich_None        .          
## hs_dde_cadj_Log2       -0.039528137
## hs_ddt_cadj_Log2        .          
## hs_hcb_cadj_Log2        .          
## hs_pcb118_cadj_Log2     .          
## hs_pcb138_cadj_Log2     .          
## hs_pcb153_cadj_Log2    -0.169008355
## hs_pcb170_cadj_Log2    -0.055808065
## hs_pcb180_cadj_Log2     .          
## hs_dep_cadj_Log2       -0.019034348
## hs_detp_cadj_Log2       .          
## hs_dmdtp_cdich_None     .          
## hs_dmp_cadj_Log2        .          
## hs_dmtp_cadj_Log2       .          
## hs_pbde153_cadj_Log2   -0.035464586
## hs_pbde47_cadj_Log2     .          
## hs_pfhxs_c_Log2        -0.006816020
## hs_pfna_c_Log2          .          
## hs_pfoa_c_Log2         -0.135997766
## hs_pfos_c_Log2         -0.047692264
## hs_pfunda_c_Log2        .          
## hs_bpa_cadj_Log2        .          
## hs_bupa_cadj_Log2       .          
## hs_etpa_cadj_Log2       .          
## hs_mepa_cadj_Log2       .          
## hs_oxbe_cadj_Log2       0.002529961
## hs_prpa_cadj_Log2       0.001735800
## hs_trcs_cadj_Log2       .          
## hs_mbzp_cadj_Log2       0.040317847
## hs_mecpp_cadj_Log2      .          
## hs_mehhp_cadj_Log2      .          
## hs_mehp_cadj_Log2       .          
## hs_meohp_cadj_Log2      .          
## hs_mep_cadj_Log2        .          
## hs_mibp_cadj_Log2      -0.047892677
## hs_mnbp_cadj_Log2      -0.008483913
## hs_ohminp_cadj_Log2     .          
## hs_oxominp_cadj_Log2    .          
## hs_cotinine_cdich_None  .          
## hs_globalexp2_None      .
cat("Model without Covariates - Test MSE:", test_mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.228805

Postnatal Diet Data

Predicting Lasso

# LASSO with train/test
set.seed(101)  
train_indices <- sample(seq_len(nrow(diet_outcome_cov)), size = floor(0.7 * nrow(diet_outcome_cov)))
test_indices <- setdiff(seq_len(nrow(diet_outcome_cov)), train_indices)

diet_data <- diet_outcome_cov[, postnatal_diet]
x_diet_train <- model.matrix(~ . + 0, data = diet_data[train_indices, ])  
x_diet_test <- model.matrix(~ . + 0, data = diet_data[test_indices, ])  

covariates <- diet_outcome_cov[, c("e3_sex_None", "e3_yearbir_None", "h_edumc_None", "h_cohort", "hs_child_age_None")]
x_covariates_train <- model.matrix(~ . + 0, data = covariates[train_indices, ]) 
x_covariates_test <- model.matrix(~ . + 0, data = covariates[test_indices, ])

x_full_train <- cbind(x_diet_train, x_covariates_train)
x_full_test <- cbind(x_diet_test, x_covariates_test)

x_full_train[is.na(x_full_train)] <- 0
x_full_test[is.na(x_full_test)] <- 0
x_diet_train[is.na(x_diet_train)] <- 0
x_diet_test[is.na(x_diet_test)] <- 0

y_train <- as.numeric(diet_outcome_cov$hs_zbmi_who[train_indices])
y_test <- as.numeric(diet_outcome_cov$hs_zbmi_who[test_indices])

# fit models
fit_without_covariates <- cv.glmnet(x_diet_train, y_train, alpha = 1, family = "gaussian")
fit_without_covariates
## 
## Call:  cv.glmnet(x = x_diet_train, y = y_train, alpha = 1, family = "gaussian") 
## 
## Measure: Mean-Squared Error 
## 
##      Lambda Index Measure      SE Nonzero
## min 0.06922     9   1.431 0.06022       5
## 1se 0.14570     1   1.442 0.06160       0
plot(fit_without_covariates, xvar = "lambda", main = "Coefficient Path (Without Covariates)")

best_lambda <- fit_without_covariates$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates, s = best_lambda)
## 41 x 1 sparse Matrix of class "dgCMatrix"
##                                         s1
## (Intercept)                     0.53256344
## h_bfdur_Ter(0,10.8]             .         
## h_bfdur_Ter(10.8,34.9]          .         
## h_bfdur_Ter(34.9,Inf]           .         
## hs_bakery_prod_Ter(2,6]         .         
## hs_bakery_prod_Ter(6,Inf]       .         
## hs_beverages_Ter(0.132,1]       .         
## hs_beverages_Ter(1,Inf]         .         
## hs_break_cer_Ter(1.1,5.5]       .         
## hs_break_cer_Ter(5.5,Inf]       .         
## hs_caff_drink_Ter(0.132,Inf]    .         
## hs_dairy_Ter(14.6,25.6]         .         
## hs_dairy_Ter(25.6,Inf]          .         
## hs_fastfood_Ter(0.132,0.5]      .         
## hs_fastfood_Ter(0.5,Inf]        .         
## hs_org_food_Ter(0.132,1]        .         
## hs_org_food_Ter(1,Inf]         -0.13588632
## hs_proc_meat_Ter(1.5,4]         .         
## hs_proc_meat_Ter(4,Inf]         .         
## hs_readymade_Ter(0.132,0.5]     .         
## hs_readymade_Ter(0.5,Inf]       .         
## hs_total_bread_Ter(7,17.5]      .         
## hs_total_bread_Ter(17.5,Inf]    .         
## hs_total_cereal_Ter(14.1,23.6]  .         
## hs_total_cereal_Ter(23.6,Inf]   .         
## hs_total_fish_Ter(1.5,3]        .         
## hs_total_fish_Ter(3,Inf]        .         
## hs_total_fruits_Ter(7,14.1]     .         
## hs_total_fruits_Ter(14.1,Inf]  -0.02481964
## hs_total_lipids_Ter(3,7]        .         
## hs_total_lipids_Ter(7,Inf]     -0.05164312
## hs_total_meat_Ter(6,9]          .         
## hs_total_meat_Ter(9,Inf]        .         
## hs_total_potatoes_Ter(3,4]      .         
## hs_total_potatoes_Ter(4,Inf]    .         
## hs_total_sweets_Ter(4.1,8.5]   -0.01594403
## hs_total_sweets_Ter(8.5,Inf]    .         
## hs_total_veg_Ter(6,8.5]         .         
## hs_total_veg_Ter(8.5,Inf]      -0.08180563
## hs_total_yog_Ter(6,8.5]         .         
## hs_total_yog_Ter(8.5,Inf]       .
predictions_without_covariates <- predict(fit_without_covariates, s = "lambda.min", newx = x_diet_test)
mse_without_covariates <- mean((y_test - predictions_without_covariates)^2)

cat("Model without Covariates - Test MSE:", mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.34942

Predicting Ridge

# RIDGE
fit_without_covariates <- cv.glmnet(x_diet_train, y_train, alpha = 0, family = "gaussian")
fit_without_covariates
## 
## Call:  cv.glmnet(x = x_diet_train, y = y_train, alpha = 0, family = "gaussian") 
## 
## Measure: Mean-Squared Error 
## 
##     Lambda Index Measure      SE Nonzero
## min   3.53    41   1.431 0.08497      40
## 1se 145.70     1   1.441 0.08233      40
plot(fit_without_covariates, xvar = "lambda", main = "Coefficient Path (Without Covariates)")

best_lambda <- fit_without_covariates$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates, s = best_lambda)
## 41 x 1 sparse Matrix of class "dgCMatrix"
##                                           s1
## (Intercept)                     0.5163069457
## h_bfdur_Ter(0,10.8]            -0.0114164662
## h_bfdur_Ter(10.8,34.9]          0.0353770607
## h_bfdur_Ter(34.9,Inf]          -0.0138651651
## hs_bakery_prod_Ter(2,6]         0.0228606785
## hs_bakery_prod_Ter(6,Inf]      -0.0268639952
## hs_beverages_Ter(0.132,1]      -0.0065939314
## hs_beverages_Ter(1,Inf]        -0.0016124215
## hs_break_cer_Ter(1.1,5.5]      -0.0034207548
## hs_break_cer_Ter(5.5,Inf]      -0.0337182186
## hs_caff_drink_Ter(0.132,Inf]   -0.0143879393
## hs_dairy_Ter(14.6,25.6]         0.0355023507
## hs_dairy_Ter(25.6,Inf]         -0.0005581647
## hs_fastfood_Ter(0.132,0.5]      0.0161761119
## hs_fastfood_Ter(0.5,Inf]       -0.0001750742
## hs_org_food_Ter(0.132,1]        0.0151677373
## hs_org_food_Ter(1,Inf]         -0.0682466785
## hs_proc_meat_Ter(1.5,4]         0.0222199344
## hs_proc_meat_Ter(4,Inf]        -0.0187135643
## hs_readymade_Ter(0.132,0.5]    -0.0013536008
## hs_readymade_Ter(0.5,Inf]       0.0105115509
## hs_total_bread_Ter(7,17.5]     -0.0035702530
## hs_total_bread_Ter(17.5,Inf]   -0.0070550360
## hs_total_cereal_Ter(14.1,23.6]  0.0082269928
## hs_total_cereal_Ter(23.6,Inf]  -0.0131001584
## hs_total_fish_Ter(1.5,3]       -0.0346609367
## hs_total_fish_Ter(3,Inf]       -0.0051749487
## hs_total_fruits_Ter(7,14.1]     0.0266413533
## hs_total_fruits_Ter(14.1,Inf]  -0.0389551124
## hs_total_lipids_Ter(3,7]       -0.0022752284
## hs_total_lipids_Ter(7,Inf]     -0.0476627593
## hs_total_meat_Ter(6,9]          0.0007524275
## hs_total_meat_Ter(9,Inf]        0.0005196923
## hs_total_potatoes_Ter(3,4]      0.0105526823
## hs_total_potatoes_Ter(4,Inf]    0.0048180175
## hs_total_sweets_Ter(4.1,8.5]   -0.0392140671
## hs_total_sweets_Ter(8.5,Inf]   -0.0010028529
## hs_total_veg_Ter(6,8.5]         0.0009962184
## hs_total_veg_Ter(8.5,Inf]      -0.0556956882
## hs_total_yog_Ter(6,8.5]        -0.0102351610
## hs_total_yog_Ter(8.5,Inf]      -0.0089303177
predictions_without_covariates <- predict(fit_without_covariates, s = "lambda.min", newx = x_diet_test)
mse_without_covariates <- mean((y_test - predictions_without_covariates)^2)

cat("Model without Covariates - Test MSE:", mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.326308

Predicting Elastic Net

#ELASTIC NET
fit_without_covariates <- cv.glmnet(x_diet_train, y_train, alpha = 0.5, family = "gaussian")
fit_without_covariates
## 
## Call:  cv.glmnet(x = x_diet_train, y = y_train, alpha = 0.5, family = "gaussian") 
## 
## Measure: Mean-Squared Error 
## 
##      Lambda Index Measure      SE Nonzero
## min 0.07218    16   1.430 0.05641      12
## 1se 0.29139     1   1.444 0.05877       0
plot(fit_without_covariates, xvar = "lambda", main = "Coefficient Path (Without Covariates)")

best_lambda <- fit_without_covariates$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates, s = best_lambda)
## 41 x 1 sparse Matrix of class "dgCMatrix"
##                                          s1
## (Intercept)                     0.650606526
## h_bfdur_Ter(0,10.8]             .          
## h_bfdur_Ter(10.8,34.9]          0.039832328
## h_bfdur_Ter(34.9,Inf]           .          
## hs_bakery_prod_Ter(2,6]         .          
## hs_bakery_prod_Ter(6,Inf]      -0.052635590
## hs_beverages_Ter(0.132,1]       .          
## hs_beverages_Ter(1,Inf]         .          
## hs_break_cer_Ter(1.1,5.5]       .          
## hs_break_cer_Ter(5.5,Inf]      -0.054788470
## hs_caff_drink_Ter(0.132,Inf]    .          
## hs_dairy_Ter(14.6,25.6]         0.053455833
## hs_dairy_Ter(25.6,Inf]          .          
## hs_fastfood_Ter(0.132,0.5]      .          
## hs_fastfood_Ter(0.5,Inf]        .          
## hs_org_food_Ter(0.132,1]        .          
## hs_org_food_Ter(1,Inf]         -0.185235916
## hs_proc_meat_Ter(1.5,4]         0.008558872
## hs_proc_meat_Ter(4,Inf]         .          
## hs_readymade_Ter(0.132,0.5]     .          
## hs_readymade_Ter(0.5,Inf]       .          
## hs_total_bread_Ter(7,17.5]      .          
## hs_total_bread_Ter(17.5,Inf]    .          
## hs_total_cereal_Ter(14.1,23.6]  .          
## hs_total_cereal_Ter(23.6,Inf]   .          
## hs_total_fish_Ter(1.5,3]       -0.057540803
## hs_total_fish_Ter(3,Inf]        .          
## hs_total_fruits_Ter(7,14.1]     0.017171763
## hs_total_fruits_Ter(14.1,Inf]  -0.054914989
## hs_total_lipids_Ter(3,7]        .          
## hs_total_lipids_Ter(7,Inf]     -0.094342286
## hs_total_meat_Ter(6,9]          .          
## hs_total_meat_Ter(9,Inf]        .          
## hs_total_potatoes_Ter(3,4]      .          
## hs_total_potatoes_Ter(4,Inf]    .          
## hs_total_sweets_Ter(4.1,8.5]   -0.089860153
## hs_total_sweets_Ter(8.5,Inf]    .          
## hs_total_veg_Ter(6,8.5]         .          
## hs_total_veg_Ter(8.5,Inf]      -0.118161721
## hs_total_yog_Ter(6,8.5]         .          
## hs_total_yog_Ter(8.5,Inf]       .
predictions_without_covariates <- predict(fit_without_covariates, s = "lambda.min", newx = x_diet_test)
mse_without_covariates <- mean((y_test - predictions_without_covariates)^2)

cat("Model without Covariates - Test MSE:", mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.335144

Combined Data (Chemicals & Postnatal Diet)

Predicting Lasso

set.seed(101)
train_indices <- sample(seq_len(nrow(interested_data)), size = floor(0.7 * nrow(interested_data)))
test_indices <- setdiff(seq_len(nrow(interested_data)), train_indices)

diet_data <- interested_data[, postnatal_diet]
x_diet_train <- model.matrix(~ . + 0, data = diet_data[train_indices, ])
x_diet_test <- model.matrix(~ . + 0, data = diet_data[test_indices, ])

chemical_data <- interested_data[, chemicals_full]
x_chemical_train <- as.matrix(chemical_data[train_indices, ])
x_chemical_test <- as.matrix(chemical_data[test_indices, ])

covariates <- interested_data[, c("e3_sex_None", "e3_yearbir_None", "h_edumc_None", "h_cohort", "hs_child_age_None")]
x_covariates_train <- model.matrix(~ . + 0, data = covariates[train_indices, ])
x_covariates_test <- model.matrix(~ . + 0, data = covariates[test_indices, ])

# combine diet and chemical data with and without covariates
x_combined_train <- cbind(x_diet_train, x_chemical_train)
x_combined_test <- cbind(x_diet_test, x_chemical_test)

x_full_train <- cbind(x_combined_train, x_covariates_train)
x_full_test <- cbind(x_combined_test, x_covariates_test)

# make sure no missing values
x_full_train[is.na(x_full_train)] <- 0
x_full_test[is.na(x_full_test)] <- 0
x_combined_train[is.na(x_combined_train)] <- 0
x_combined_test[is.na(x_combined_test)] <- 0

y_train <- as.numeric(interested_data$hs_zbmi_who[train_indices])
y_test <- as.numeric(interested_data$hs_zbmi_who[test_indices])

# LASSO
fit_without_covariates <- cv.glmnet(x_combined_train, y_train, alpha = 1, family = "gaussian")
predictions_without_covariates <- predict(fit_without_covariates, s = "lambda.min", newx = x_combined_test)
mse_without_covariates <- mean((y_test - predictions_without_covariates)^2)

plot(fit_without_covariates, xvar = "lambda", main = "Coefficient Path (Without Covariates)")

best_lambda <- fit_without_covariates$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates, s = best_lambda)
## 90 x 1 sparse Matrix of class "dgCMatrix"
##                                          s1
## (Intercept)                    -5.016149911
## h_bfdur_Ter(0,10.8]            -0.129594522
## h_bfdur_Ter(10.8,34.9]          .          
## h_bfdur_Ter(34.9,Inf]           .          
## hs_bakery_prod_Ter(2,6]         .          
## hs_bakery_prod_Ter(6,Inf]      -0.217291423
## hs_beverages_Ter(0.132,1]       .          
## hs_beverages_Ter(1,Inf]         .          
## hs_break_cer_Ter(1.1,5.5]       .          
## hs_break_cer_Ter(5.5,Inf]       .          
## hs_caff_drink_Ter(0.132,Inf]    .          
## hs_dairy_Ter(14.6,25.6]         0.009808165
## hs_dairy_Ter(25.6,Inf]          .          
## hs_fastfood_Ter(0.132,0.5]      0.070972556
## hs_fastfood_Ter(0.5,Inf]        .          
## hs_org_food_Ter(0.132,1]        .          
## hs_org_food_Ter(1,Inf]          .          
## hs_proc_meat_Ter(1.5,4]         .          
## hs_proc_meat_Ter(4,Inf]         .          
## hs_readymade_Ter(0.132,0.5]     .          
## hs_readymade_Ter(0.5,Inf]       0.011160944
## hs_total_bread_Ter(7,17.5]     -0.010168208
## hs_total_bread_Ter(17.5,Inf]    .          
## hs_total_cereal_Ter(14.1,23.6]  .          
## hs_total_cereal_Ter(23.6,Inf]   .          
## hs_total_fish_Ter(1.5,3]       -0.024288530
## hs_total_fish_Ter(3,Inf]        .          
## hs_total_fruits_Ter(7,14.1]     .          
## hs_total_fruits_Ter(14.1,Inf]  -0.016129393
## hs_total_lipids_Ter(3,7]        .          
## hs_total_lipids_Ter(7,Inf]     -0.047350302
## hs_total_meat_Ter(6,9]          .          
## hs_total_meat_Ter(9,Inf]        .          
## hs_total_potatoes_Ter(3,4]      0.018317955
## hs_total_potatoes_Ter(4,Inf]    .          
## hs_total_sweets_Ter(4.1,8.5]   -0.006515994
## hs_total_sweets_Ter(8.5,Inf]    .          
## hs_total_veg_Ter(6,8.5]         .          
## hs_total_veg_Ter(8.5,Inf]      -0.041036632
## hs_total_yog_Ter(6,8.5]         .          
## hs_total_yog_Ter(8.5,Inf]       .          
## hs_as_c_Log2                    .          
## hs_cd_c_Log2                   -0.022337287
## hs_co_c_Log2                   -0.003616434
## hs_cs_c_Log2                    0.070483114
## hs_cu_c_Log2                    0.656568320
## hs_hg_c_Log2                   -0.012267249
## hs_mn_c_Log2                    .          
## hs_mo_c_Log2                   -0.097496432
## hs_pb_c_Log2                    .          
## hs_tl_cdich_None                .          
## hs_dde_cadj_Log2               -0.029771276
## hs_ddt_cadj_Log2                .          
## hs_hcb_cadj_Log2                .          
## hs_pcb118_cadj_Log2             .          
## hs_pcb138_cadj_Log2             .          
## hs_pcb153_cadj_Log2            -0.226942147
## hs_pcb170_cadj_Log2            -0.054403335
## hs_pcb180_cadj_Log2             .          
## hs_dep_cadj_Log2               -0.017878387
## hs_detp_cadj_Log2               .          
## hs_dmdtp_cdich_None             .          
## hs_dmp_cadj_Log2                .          
## hs_dmtp_cadj_Log2               .          
## hs_pbde153_cadj_Log2           -0.035568595
## hs_pbde47_cadj_Log2             .          
## hs_pfhxs_c_Log2                 .          
## hs_pfna_c_Log2                  .          
## hs_pfoa_c_Log2                 -0.125219198
## hs_pfos_c_Log2                 -0.047655946
## hs_pfunda_c_Log2                .          
## hs_bpa_cadj_Log2                .          
## hs_bupa_cadj_Log2               .          
## hs_etpa_cadj_Log2               .          
## hs_mepa_cadj_Log2               .          
## hs_oxbe_cadj_Log2               .          
## hs_prpa_cadj_Log2               .          
## hs_trcs_cadj_Log2               .          
## hs_mbzp_cadj_Log2               0.043689764
## hs_mecpp_cadj_Log2              .          
## hs_mehhp_cadj_Log2              .          
## hs_mehp_cadj_Log2               .          
## hs_meohp_cadj_Log2              .          
## hs_mep_cadj_Log2                .          
## hs_mibp_cadj_Log2              -0.040902710
## hs_mnbp_cadj_Log2              -0.007173325
## hs_ohminp_cadj_Log2             .          
## hs_oxominp_cadj_Log2            .          
## hs_cotinine_cdich_None          .          
## hs_globalexp2_None              .
cat("Model without Covariates - Test MSE:", mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.200253

Predicting Ridge

# RIDGE
fit_without_covariates <- cv.glmnet(x_combined_train, y_train, alpha = 0, family = "gaussian")
predictions_without_covariates <- predict(fit_without_covariates, s = "lambda.min", newx = x_combined_test)
mse_without_covariates <- mean((y_test - predictions_without_covariates)^2)

plot(fit_without_covariates, xvar = "lambda", main = "Coefficient Path (Without Covariates)")

best_lambda <- fit_without_covariates$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates, s = best_lambda)
## 90 x 1 sparse Matrix of class "dgCMatrix"
##                                           s1
## (Intercept)                    -3.7486876482
## h_bfdur_Ter(0,10.8]            -0.0862270481
## h_bfdur_Ter(10.8,34.9]          0.0187498222
## h_bfdur_Ter(34.9,Inf]           0.0718972907
## hs_bakery_prod_Ter(2,6]        -0.0033853186
## hs_bakery_prod_Ter(6,Inf]      -0.1580980396
## hs_beverages_Ter(0.132,1]       0.0052318976
## hs_beverages_Ter(1,Inf]        -0.0339118523
## hs_break_cer_Ter(1.1,5.5]       0.0042988311
## hs_break_cer_Ter(5.5,Inf]      -0.0503391950
## hs_caff_drink_Ter(0.132,Inf]    0.0156001183
## hs_dairy_Ter(14.6,25.6]         0.0416574408
## hs_dairy_Ter(25.6,Inf]         -0.0174860568
## hs_fastfood_Ter(0.132,0.5]      0.0650667870
## hs_fastfood_Ter(0.5,Inf]       -0.0300919849
## hs_org_food_Ter(0.132,1]        0.0284491409
## hs_org_food_Ter(1,Inf]         -0.0490021669
## hs_proc_meat_Ter(1.5,4]         0.0055207383
## hs_proc_meat_Ter(4,Inf]        -0.0063080789
## hs_readymade_Ter(0.132,0.5]     0.0307292842
## hs_readymade_Ter(0.5,Inf]       0.0632539981
## hs_total_bread_Ter(7,17.5]     -0.0544944827
## hs_total_bread_Ter(17.5,Inf]    0.0146129335
## hs_total_cereal_Ter(14.1,23.6] -0.0004875292
## hs_total_cereal_Ter(23.6,Inf]   0.0180167268
## hs_total_fish_Ter(1.5,3]       -0.0683250014
## hs_total_fish_Ter(3,Inf]        0.0112125503
## hs_total_fruits_Ter(7,14.1]     0.0353241028
## hs_total_fruits_Ter(14.1,Inf]  -0.0433100932
## hs_total_lipids_Ter(3,7]       -0.0171427895
## hs_total_lipids_Ter(7,Inf]     -0.0848619938
## hs_total_meat_Ter(6,9]          0.0172861408
## hs_total_meat_Ter(9,Inf]        0.0044053472
## hs_total_potatoes_Ter(3,4]      0.0536415284
## hs_total_potatoes_Ter(4,Inf]   -0.0115575388
## hs_total_sweets_Ter(4.1,8.5]   -0.0692484887
## hs_total_sweets_Ter(8.5,Inf]   -0.0097071229
## hs_total_veg_Ter(6,8.5]         0.0031586461
## hs_total_veg_Ter(8.5,Inf]      -0.0567605211
## hs_total_yog_Ter(6,8.5]        -0.0245534422
## hs_total_yog_Ter(8.5,Inf]      -0.0386998840
## hs_as_c_Log2                    0.0050439215
## hs_cd_c_Log2                   -0.0352737869
## hs_co_c_Log2                   -0.0396473666
## hs_cs_c_Log2                    0.0905666600
## hs_cu_c_Log2                    0.5291861050
## hs_hg_c_Log2                   -0.0253437065
## hs_mn_c_Log2                   -0.0187832842
## hs_mo_c_Log2                   -0.0835328881
## hs_pb_c_Log2                   -0.0275390915
## hs_tl_cdich_None                .           
## hs_dde_cadj_Log2               -0.0366806354
## hs_ddt_cadj_Log2                0.0032185740
## hs_hcb_cadj_Log2               -0.0317509983
## hs_pcb118_cadj_Log2             0.0025521400
## hs_pcb138_cadj_Log2            -0.0518399321
## hs_pcb153_cadj_Log2            -0.1215197442
## hs_pcb170_cadj_Log2            -0.0418593821
## hs_pcb180_cadj_Log2            -0.0225049584
## hs_dep_cadj_Log2               -0.0189572104
## hs_detp_cadj_Log2               0.0059280868
## hs_dmdtp_cdich_None             .           
## hs_dmp_cadj_Log2               -0.0024527279
## hs_dmtp_cadj_Log2               0.0008420662
## hs_pbde153_cadj_Log2           -0.0277474044
## hs_pbde47_cadj_Log2             0.0052481134
## hs_pfhxs_c_Log2                -0.0305593699
## hs_pfna_c_Log2                 -0.0041077407
## hs_pfoa_c_Log2                 -0.1108211867
## hs_pfos_c_Log2                 -0.0475012252
## hs_pfunda_c_Log2                0.0072385180
## hs_bpa_cadj_Log2               -0.0063616978
## hs_bupa_cadj_Log2               0.0036910227
## hs_etpa_cadj_Log2              -0.0049963326
## hs_mepa_cadj_Log2              -0.0096168009
## hs_oxbe_cadj_Log2               0.0101184198
## hs_prpa_cadj_Log2               0.0061492375
## hs_trcs_cadj_Log2               0.0062007460
## hs_mbzp_cadj_Log2               0.0427566149
## hs_mecpp_cadj_Log2              0.0064702943
## hs_mehhp_cadj_Log2              0.0137458333
## hs_mehp_cadj_Log2              -0.0049569930
## hs_meohp_cadj_Log2              0.0093327409
## hs_mep_cadj_Log2                0.0064280760
## hs_mibp_cadj_Log2              -0.0385576131
## hs_mnbp_cadj_Log2              -0.0344895032
## hs_ohminp_cadj_Log2            -0.0210558232
## hs_oxominp_cadj_Log2            0.0113725933
## hs_cotinine_cdich_None          .           
## hs_globalexp2_None              .
cat("Model without Covariates - Test MSE:", mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.154844

Predicting Elastic Net

# ELASTIC NET
fit_without_covariates <- cv.glmnet(x_combined_train, y_train, alpha = 0.5, family = "gaussian")
predictions_without_covariates <- predict(fit_without_covariates, s = "lambda.min", newx = x_combined_test)
mse_without_covariates <- mean((y_test - predictions_without_covariates)^2)

plot(fit_without_covariates, xvar = "lambda", main = "Coefficient Path (Without Covariates)")

best_lambda <- fit_without_covariates$lambda.min  # lambda that minimizes the MSE
coef(fit_without_covariates, s = best_lambda)
## 90 x 1 sparse Matrix of class "dgCMatrix"
##                                           s1
## (Intercept)                    -5.0446731390
## h_bfdur_Ter(0,10.8]            -0.1251508851
## h_bfdur_Ter(10.8,34.9]          .           
## h_bfdur_Ter(34.9,Inf]           0.0089409662
## hs_bakery_prod_Ter(2,6]         .           
## hs_bakery_prod_Ter(6,Inf]      -0.2141179309
## hs_beverages_Ter(0.132,1]       .           
## hs_beverages_Ter(1,Inf]         .           
## hs_break_cer_Ter(1.1,5.5]       .           
## hs_break_cer_Ter(5.5,Inf]       .           
## hs_caff_drink_Ter(0.132,Inf]    .           
## hs_dairy_Ter(14.6,25.6]         0.0175630268
## hs_dairy_Ter(25.6,Inf]          .           
## hs_fastfood_Ter(0.132,0.5]      0.0739162130
## hs_fastfood_Ter(0.5,Inf]        .           
## hs_org_food_Ter(0.132,1]        .           
## hs_org_food_Ter(1,Inf]         -0.0049809964
## hs_proc_meat_Ter(1.5,4]         .           
## hs_proc_meat_Ter(4,Inf]         .           
## hs_readymade_Ter(0.132,0.5]     .           
## hs_readymade_Ter(0.5,Inf]       0.0170253867
## hs_total_bread_Ter(7,17.5]     -0.0178078486
## hs_total_bread_Ter(17.5,Inf]    .           
## hs_total_cereal_Ter(14.1,23.6]  .           
## hs_total_cereal_Ter(23.6,Inf]   .           
## hs_total_fish_Ter(1.5,3]       -0.0311197485
## hs_total_fish_Ter(3,Inf]        .           
## hs_total_fruits_Ter(7,14.1]     0.0058224545
## hs_total_fruits_Ter(14.1,Inf]  -0.0180115810
## hs_total_lipids_Ter(3,7]        .           
## hs_total_lipids_Ter(7,Inf]     -0.0529611086
## hs_total_meat_Ter(6,9]          .           
## hs_total_meat_Ter(9,Inf]        .           
## hs_total_potatoes_Ter(3,4]      0.0233163117
## hs_total_potatoes_Ter(4,Inf]    .           
## hs_total_sweets_Ter(4.1,8.5]   -0.0128007469
## hs_total_sweets_Ter(8.5,Inf]    .           
## hs_total_veg_Ter(6,8.5]         .           
## hs_total_veg_Ter(8.5,Inf]      -0.0436127333
## hs_total_yog_Ter(6,8.5]         .           
## hs_total_yog_Ter(8.5,Inf]       .           
## hs_as_c_Log2                    .           
## hs_cd_c_Log2                   -0.0242086233
## hs_co_c_Log2                   -0.0084586207
## hs_cs_c_Log2                    0.0772668783
## hs_cu_c_Log2                    0.6571106900
## hs_hg_c_Log2                   -0.0143619887
## hs_mn_c_Log2                    .           
## hs_mo_c_Log2                   -0.0974389913
## hs_pb_c_Log2                    .           
## hs_tl_cdich_None                .           
## hs_dde_cadj_Log2               -0.0321212412
## hs_ddt_cadj_Log2                .           
## hs_hcb_cadj_Log2                .           
## hs_pcb118_cadj_Log2             .           
## hs_pcb138_cadj_Log2             .           
## hs_pcb153_cadj_Log2            -0.2221589832
## hs_pcb170_cadj_Log2            -0.0546331904
## hs_pcb180_cadj_Log2             .           
## hs_dep_cadj_Log2               -0.0179999867
## hs_detp_cadj_Log2               .           
## hs_dmdtp_cdich_None             .           
## hs_dmp_cadj_Log2                .           
## hs_dmtp_cadj_Log2               .           
## hs_pbde153_cadj_Log2           -0.0351341084
## hs_pbde47_cadj_Log2             .           
## hs_pfhxs_c_Log2                -0.0055363055
## hs_pfna_c_Log2                  .           
## hs_pfoa_c_Log2                 -0.1254532888
## hs_pfos_c_Log2                 -0.0469893259
## hs_pfunda_c_Log2                .           
## hs_bpa_cadj_Log2                .           
## hs_bupa_cadj_Log2               .           
## hs_etpa_cadj_Log2               .           
## hs_mepa_cadj_Log2               .           
## hs_oxbe_cadj_Log2               .           
## hs_prpa_cadj_Log2               0.0001965683
## hs_trcs_cadj_Log2               .           
## hs_mbzp_cadj_Log2               0.0457827093
## hs_mecpp_cadj_Log2              .           
## hs_mehhp_cadj_Log2              .           
## hs_mehp_cadj_Log2               .           
## hs_meohp_cadj_Log2              .           
## hs_mep_cadj_Log2                .           
## hs_mibp_cadj_Log2              -0.0415220843
## hs_mnbp_cadj_Log2              -0.0111086286
## hs_ohminp_cadj_Log2             .           
## hs_oxominp_cadj_Log2            .           
## hs_cotinine_cdich_None          .           
## hs_globalexp2_None              .
cat("Model without Covariates - Test MSE:", mse_without_covariates, "\n")
## Model without Covariates - Test MSE: 1.198308

Finalized Data

Selected data based on the enet features without covariates.

Still trying to decide if to stick with continuous or dichotomous outcome (for sensitivity/specificity). Will try to freeze the covariates in the lasso, ridge, or enet.

#selected chemicals that were noted in enet
chemicals_selected <- c(
  "hs_cd_c_Log2",
  "hs_co_c_Log2",
  "hs_cs_c_Log2",
  "hs_cu_c_Log2",
  "hs_hg_c_Log2",
  "hs_mo_c_Log2",
  "hs_pb_c_Log2",
  "hs_dde_cadj_Log2",
  "hs_pcb153_cadj_Log2",
  "hs_pcb170_cadj_Log2",
  "hs_dep_cadj_Log2",
  "hs_detp_cadj_Log2",
  "hs_pbde153_cadj_Log2",
  "hs_pfhxs_c_Log2",
  "hs_pfoa_c_Log2",
  "hs_pfos_c_Log2",
  "hs_mepa_cadj_Log2",
  "hs_oxbe_cadj_Log2",
  "hs_prpa_cadj_Log2",
  "hs_mbzp_cadj_Log2",
  "hs_mibp_cadj_Log2",
  "hs_mnbp_cadj_Log2")
#selected diets that were noted in enet
diet_selected <- c(
  "h_bfdur_Ter",
  "hs_bakery_prod_Ter",
  "hs_break_cer_Ter",
  "hs_dairy_Ter",
  "hs_fastfood_Ter",
  "hs_org_food_Ter",
  "hs_proc_meat_Ter",
  "hs_total_fish_Ter",
  "hs_total_fruits_Ter",
  "hs_total_lipids_Ter",
  "hs_total_sweets_Ter",
  "hs_total_veg_Ter"
)
combined_data_selected <- c(
  "h_bfdur_Ter",
  "hs_bakery_prod_Ter",
  "hs_dairy_Ter",
  "hs_fastfood_Ter",
  "hs_org_food_Ter",
  "hs_readymade_Ter",
  "hs_total_bread_Ter",
  "hs_total_fish_Ter",
  "hs_total_fruits_Ter",
  "hs_total_lipids_Ter",
  "hs_total_potatoes_Ter",
  "hs_total_sweets_Ter",
  "hs_total_veg_Ter",
  "hs_cd_c_Log2",
  "hs_co_c_Log2",
  "hs_cs_c_Log2",
  "hs_cu_c_Log2",
  "hs_hg_c_Log2",
  "hs_mo_c_Log2",
  "hs_pb_c_Log2",
  "hs_dde_cadj_Log2",
  "hs_pcb153_cadj_Log2",
  "hs_pcb170_cadj_Log2",
  "hs_dep_cadj_Log2",
  "hs_pbde153_cadj_Log2",
  "hs_pfhxs_c_Log2",
  "hs_pfoa_c_Log2",
  "hs_pfos_c_Log2",
  "hs_prpa_cadj_Log2",
  "hs_mbzp_cadj_Log2",
  "hs_mibp_cadj_Log2",
  "hs_mnbp_cadj_Log2"
)

outcome_cov <- cbind(covariate_data, outcome_BMI)
outcome_cov <- outcome_cov[, !duplicated(colnames(outcome_cov))]

finalized_columns <- c(combined_data_selected)
final_selected_data <- exposome %>% dplyr::select(all_of(finalized_columns))

finalized_data <- cbind(outcome_cov, final_selected_data)
head(finalized_data)
numeric_vars <- finalized_data %>%
  dplyr::select(where(is.numeric))

cor_matrix <- cor(numeric_vars, use = "complete.obs")
corrplot(cor_matrix, method = "color", type = "upper", tl.col = "black", tl.srt = 60, tl.cex = 0.8)

set.seed(101)

# Splitting data into training and test sets
train_indices <- sample(seq_len(nrow(finalized_data)), size = floor(0.7 * nrow(finalized_data)))
test_indices <- setdiff(seq_len(nrow(finalized_data)), train_indices)

# Creating training and test datasets
train_data <- finalized_data[train_indices, ]
test_data <- finalized_data[test_indices, ]

# Separating predictors and outcome variable
x_train <- model.matrix(~ . + 0, data = train_data[ , !names(train_data) %in% "hs_zbmi_who"])
x_test <- model.matrix(~ . + 0, data = test_data[ , !names(test_data) %in% "hs_zbmi_who"])
y_train <- train_data$hs_zbmi_who
y_test <- test_data$hs_zbmi_who

LASSO

fit_lasso <- cv.glmnet(x_train, y_train, alpha = 1, family = "gaussian")
plot(fit_lasso, xvar = "lambda", main = "Coefficients Path")

best_lambda <- fit_lasso$lambda.min
coef(fit_lasso, s = best_lambda)
## 62 x 1 sparse Matrix of class "dgCMatrix"
##                                         s1
## (Intercept)                   -6.056529401
## e3_sex_Nonefemale             -0.168363086
## e3_sex_Nonemale                .          
## e3_yearbir_None2004           -0.108416038
## e3_yearbir_None2005            0.015830408
## e3_yearbir_None2006            .          
## e3_yearbir_None2007            .          
## e3_yearbir_None2008            .          
## e3_yearbir_None2009            .          
## h_edumc_None2                  .          
## h_edumc_None3                  0.024936478
## h_cohort2                     -0.065001689
## h_cohort3                      0.498485647
## h_cohort4                      0.448839670
## h_cohort5                      .          
## h_cohort6                      0.274566775
## hs_child_age_None              .          
## h_bfdur_Ter(10.8,34.9]         0.009853977
## h_bfdur_Ter(34.9,Inf]          0.206688198
## hs_bakery_prod_Ter(2,6]       -0.079379910
## hs_bakery_prod_Ter(6,Inf]     -0.287940431
## hs_dairy_Ter(14.6,25.6]        0.036305012
## hs_dairy_Ter(25.6,Inf]         .          
## hs_fastfood_Ter(0.132,0.5]     0.087371043
## hs_fastfood_Ter(0.5,Inf]       .          
## hs_org_food_Ter(0.132,1]       0.014758429
## hs_org_food_Ter(1,Inf]        -0.003334294
## hs_readymade_Ter(0.132,0.5]    .          
## hs_readymade_Ter(0.5,Inf]      0.055235035
## hs_total_bread_Ter(7,17.5]    -0.086581886
## hs_total_bread_Ter(17.5,Inf]   0.006856624
## hs_total_fish_Ter(1.5,3]      -0.014098467
## hs_total_fish_Ter(3,Inf]       .          
## hs_total_fruits_Ter(7,14.1]    0.019842672
## hs_total_fruits_Ter(14.1,Inf] -0.002110980
## hs_total_lipids_Ter(3,7]       .          
## hs_total_lipids_Ter(7,Inf]    -0.029588146
## hs_total_potatoes_Ter(3,4]     0.019966856
## hs_total_potatoes_Ter(4,Inf]   .          
## hs_total_sweets_Ter(4.1,8.5]  -0.048986632
## hs_total_sweets_Ter(8.5,Inf]   .          
## hs_total_veg_Ter(6,8.5]        .          
## hs_total_veg_Ter(8.5,Inf]     -0.012007741
## hs_cd_c_Log2                  -0.021414266
## hs_co_c_Log2                  -0.022114848
## hs_cs_c_Log2                   0.213157355
## hs_cu_c_Log2                   0.788079558
## hs_hg_c_Log2                  -0.029736248
## hs_mo_c_Log2                  -0.106918910
## hs_pb_c_Log2                  -0.046230061
## hs_dde_cadj_Log2              -0.064720561
## hs_pcb153_cadj_Log2           -0.313021060
## hs_pcb170_cadj_Log2           -0.061190488
## hs_dep_cadj_Log2              -0.018332035
## hs_pbde153_cadj_Log2          -0.030575626
## hs_pfhxs_c_Log2                .          
## hs_pfoa_c_Log2                -0.128583627
## hs_pfos_c_Log2                 .          
## hs_prpa_cadj_Log2              .          
## hs_mbzp_cadj_Log2              0.063851782
## hs_mibp_cadj_Log2             -0.044082983
## hs_mnbp_cadj_Log2             -0.017333893
predictions_lasso <- predict(fit_lasso, s = "lambda.min", newx = x_test)
mse_lasso <- mean((y_test - predictions_lasso)^2)
rmse_lasso <- sqrt(mse_lasso)

roc_lasso <- roc(y_test, predictions_lasso)
## Setting levels: control = -3.58, case = -2.22
## Setting direction: controls < cases
auc_lasso <- auc(roc_lasso)

cat("Lasso Test MSE:", mse_lasso, "\n")
## Lasso Test MSE: 1.161457
cat("Lasso Test RMSE:", rmse_lasso, "\n")
## Lasso Test RMSE: 1.077709
cat("Lasso Test AUC:", auc_lasso)
## Lasso Test AUC: 1
plot(roc_lasso, main = "ROC Curve (Lasso)")

Ridge

fit_ridge <- cv.glmnet(x_train, y_train, alpha = 0, family = "gaussian")
plot(fit_ridge, xvar = "lambda", main = "Coefficients Path")

best_lambda <- fit_ridge$lambda.min
coef(fit_ridge, s = best_lambda)
## 62 x 1 sparse Matrix of class "dgCMatrix"
##                                         s1
## (Intercept)                   -5.506665822
## e3_sex_Nonefemale             -0.087702836
## e3_sex_Nonemale                0.087402624
## e3_yearbir_None2004           -0.116309944
## e3_yearbir_None2005            0.056970622
## e3_yearbir_None2006           -0.018414120
## e3_yearbir_None2007            0.021957431
## e3_yearbir_None2008            0.025846916
## e3_yearbir_None2009            0.030936201
## h_edumc_None2                  0.055212238
## h_edumc_None3                  0.068414042
## h_cohort2                     -0.125274663
## h_cohort3                      0.317193746
## h_cohort4                      0.292921048
## h_cohort5                     -0.025263276
## h_cohort6                      0.193660644
## hs_child_age_None             -0.010836848
## h_bfdur_Ter(10.8,34.9]         0.045883632
## h_bfdur_Ter(34.9,Inf]          0.173946349
## hs_bakery_prod_Ter(2,6]       -0.077881239
## hs_bakery_prod_Ter(6,Inf]     -0.239808801
## hs_dairy_Ter(14.6,25.6]        0.067133380
## hs_dairy_Ter(25.6,Inf]         0.006026921
## hs_fastfood_Ter(0.132,0.5]     0.082209045
## hs_fastfood_Ter(0.5,Inf]      -0.020476480
## hs_org_food_Ter(0.132,1]       0.017363627
## hs_org_food_Ter(1,Inf]        -0.044193460
## hs_readymade_Ter(0.132,0.5]    0.040152728
## hs_readymade_Ter(0.5,Inf]      0.090677701
## hs_total_bread_Ter(7,17.5]    -0.091649770
## hs_total_bread_Ter(17.5,Inf]   0.027788762
## hs_total_fish_Ter(1.5,3]      -0.061716572
## hs_total_fish_Ter(3,Inf]      -0.021700771
## hs_total_fruits_Ter(7,14.1]    0.035358675
## hs_total_fruits_Ter(14.1,Inf] -0.028781089
## hs_total_lipids_Ter(3,7]      -0.011001748
## hs_total_lipids_Ter(7,Inf]    -0.060711731
## hs_total_potatoes_Ter(3,4]     0.035711239
## hs_total_potatoes_Ter(4,Inf]   0.001734892
## hs_total_sweets_Ter(4.1,8.5]  -0.077820901
## hs_total_sweets_Ter(8.5,Inf]  -0.007782675
## hs_total_veg_Ter(6,8.5]        0.010704282
## hs_total_veg_Ter(8.5,Inf]     -0.033156441
## hs_cd_c_Log2                  -0.035319275
## hs_co_c_Log2                  -0.044529238
## hs_cs_c_Log2                   0.202597863
## hs_cu_c_Log2                   0.713939861
## hs_hg_c_Log2                  -0.029266725
## hs_mo_c_Log2                  -0.105371823
## hs_pb_c_Log2                  -0.043118149
## hs_dde_cadj_Log2              -0.069459637
## hs_pcb153_cadj_Log2           -0.246311891
## hs_pcb170_cadj_Log2           -0.059596050
## hs_dep_cadj_Log2              -0.019299041
## hs_pbde153_cadj_Log2          -0.031005364
## hs_pfhxs_c_Log2               -0.002098677
## hs_pfoa_c_Log2                -0.145681432
## hs_pfos_c_Log2                -0.019471004
## hs_prpa_cadj_Log2              0.001734861
## hs_mbzp_cadj_Log2              0.066326947
## hs_mibp_cadj_Log2             -0.041795405
## hs_mnbp_cadj_Log2             -0.036158552
predictions_ridge <- predict(fit_ridge, s = "lambda.min", newx = x_test)
mse_ridge <- mean((y_test - predictions_ridge)^2)
rmse_ridge <- sqrt(mse_ridge)

roc_ridge <- roc(y_test, predictions_ridge)
## Setting levels: control = -3.58, case = -2.22
## Setting direction: controls < cases
auc_ridge <- auc(roc_ridge)

cat("Ridge Test MSE:", mse_ridge, "\n")
## Ridge Test MSE: 1.150747
cat("Ridge Test RMSE:", rmse_ridge, "\n")
## Ridge Test RMSE: 1.072729
cat("Ridge Test AUC:", auc_ridge, "\n")
## Ridge Test AUC: 1
plot(roc_ridge, main = "ROC Curve (Ridge)")

Elastic Net

fit_enet <- cv.glmnet(x_train, y_train, alpha = 0.5, family = "gaussian")
plot(fit_enet, xvar = "lambda", main = "Coefficients Path")

best_lambda <- fit_enet$lambda.min
coef(fit_enet, s = best_lambda)
## 62 x 1 sparse Matrix of class "dgCMatrix"
##                                         s1
## (Intercept)                   -6.135902449
## e3_sex_Nonefemale             -0.091328664
## e3_sex_Nonemale                0.078356308
## e3_yearbir_None2004           -0.106629256
## e3_yearbir_None2005            0.020246640
## e3_yearbir_None2006            .          
## e3_yearbir_None2007            .          
## e3_yearbir_None2008            .          
## e3_yearbir_None2009            .          
## h_edumc_None2                  .          
## h_edumc_None3                  0.026571071
## h_cohort2                     -0.080139872
## h_cohort3                      0.478028559
## h_cohort4                      0.438891150
## h_cohort5                      .          
## h_cohort6                      0.267851096
## hs_child_age_None              .          
## h_bfdur_Ter(10.8,34.9]         0.015076770
## h_bfdur_Ter(34.9,Inf]          0.205015743
## hs_bakery_prod_Ter(2,6]       -0.080046803
## hs_bakery_prod_Ter(6,Inf]     -0.284248988
## hs_dairy_Ter(14.6,25.6]        0.039639471
## hs_dairy_Ter(25.6,Inf]         .          
## hs_fastfood_Ter(0.132,0.5]     0.088885113
## hs_fastfood_Ter(0.5,Inf]       .          
## hs_org_food_Ter(0.132,1]       0.013880043
## hs_org_food_Ter(1,Inf]        -0.008246874
## hs_readymade_Ter(0.132,0.5]    .          
## hs_readymade_Ter(0.5,Inf]      0.056877061
## hs_total_bread_Ter(7,17.5]    -0.087779515
## hs_total_bread_Ter(17.5,Inf]   0.008235596
## hs_total_fish_Ter(1.5,3]      -0.018480536
## hs_total_fish_Ter(3,Inf]       .          
## hs_total_fruits_Ter(7,14.1]    0.020734197
## hs_total_fruits_Ter(14.1,Inf] -0.005694289
## hs_total_lipids_Ter(3,7]       .          
## hs_total_lipids_Ter(7,Inf]    -0.032924994
## hs_total_potatoes_Ter(3,4]     0.020685984
## hs_total_potatoes_Ter(4,Inf]   .          
## hs_total_sweets_Ter(4.1,8.5]  -0.051802913
## hs_total_sweets_Ter(8.5,Inf]   .          
## hs_total_veg_Ter(6,8.5]        .          
## hs_total_veg_Ter(8.5,Inf]     -0.014437172
## hs_cd_c_Log2                  -0.023265047
## hs_co_c_Log2                  -0.024387720
## hs_cs_c_Log2                   0.213269641
## hs_cu_c_Log2                   0.787050001
## hs_hg_c_Log2                  -0.030166372
## hs_mo_c_Log2                  -0.107397502
## hs_pb_c_Log2                  -0.045306072
## hs_dde_cadj_Log2              -0.065275097
## hs_pcb153_cadj_Log2           -0.308430760
## hs_pcb170_cadj_Log2           -0.061445158
## hs_dep_cadj_Log2              -0.018623289
## hs_pbde153_cadj_Log2          -0.030728037
## hs_pfhxs_c_Log2                .          
## hs_pfoa_c_Log2                -0.131846844
## hs_pfos_c_Log2                 .          
## hs_prpa_cadj_Log2              .          
## hs_mbzp_cadj_Log2              0.065135803
## hs_mibp_cadj_Log2             -0.043589996
## hs_mnbp_cadj_Log2             -0.020027202
predictions_enet <- predict(fit_enet, s = "lambda.min", newx = x_test)
mse_enet <- mean((y_test - predictions_enet)^2)
rmse_enet <- sqrt(mse_enet)

roc_enet <- roc(y_test, predictions_enet)
## Setting levels: control = -3.58, case = -2.22
## Setting direction: controls < cases
auc_enet <- auc(roc_enet)

cat("Elastic Net Test MSE:", mse_enet, "\n")
## Elastic Net Test MSE: 1.161523
cat("Elastic Net Test RMSE:", rmse_enet, "\n")
## Elastic Net Test RMSE: 1.07774
cat("Elastic Net Test AUC:", auc_enet, "\n")
## Elastic Net Test AUC: 1
plot(roc_enet, main = "ROC Curve (Elastic Net)")

Random Forest

rf_model <- randomForest(x_train, y_train, ntree=500, importance=TRUE)
predictions_rf <- predict(rf_model, x_test)
mse_rf <- mean((y_test - predictions_rf)^2)
rmse_rf <- sqrt(mse_rf)

roc_rf <- roc(y_test, predictions_rf)
## Setting levels: control = -3.58, case = -2.22
## Setting direction: controls < cases
auc_rf <- auc(roc_rf)

cat("Random Forest Test MSE:", mse_rf, "\n")
## Random Forest Test MSE: 1.143216
cat("Random Forest Test RMSE:", rmse_rf, "\n")
## Random Forest Test RMSE: 1.069213
cat("Random Forest Test AUC:", auc_rf, "\n")
## Random Forest Test AUC: 1
plot(roc_rf, main = "ROC Curve (Random Forest)")

varImpPlot(rf_model)

GBM

gbm_model <- gbm(hs_zbmi_who ~ ., data = train_data, 
                 distribution = "gaussian",
                 n.trees = 1000,
                 interaction.depth = 3,
                 n.minobsinnode = 10,
                 shrinkage = 0.01,
                 cv.folds = 5,
                 verbose = TRUE)
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        1.4330             nan     0.0100    0.0039
##      2        1.4294             nan     0.0100    0.0031
##      3        1.4260             nan     0.0100    0.0018
##      4        1.4230             nan     0.0100    0.0016
##      5        1.4183             nan     0.0100    0.0036
##      6        1.4144             nan     0.0100    0.0042
##      7        1.4102             nan     0.0100    0.0033
##      8        1.4064             nan     0.0100    0.0032
##      9        1.4018             nan     0.0100    0.0039
##     10        1.3984             nan     0.0100    0.0027
##     20        1.3622             nan     0.0100    0.0020
##     40        1.3002             nan     0.0100    0.0015
##     60        1.2525             nan     0.0100    0.0007
##     80        1.2121             nan     0.0100    0.0013
##    100        1.1770             nan     0.0100    0.0008
##    120        1.1461             nan     0.0100    0.0002
##    140        1.1191             nan     0.0100   -0.0000
##    160        1.0942             nan     0.0100    0.0002
##    180        1.0718             nan     0.0100    0.0007
##    200        1.0511             nan     0.0100    0.0003
##    220        1.0334             nan     0.0100   -0.0001
##    240        1.0163             nan     0.0100   -0.0001
##    260        1.0010             nan     0.0100   -0.0000
##    280        0.9857             nan     0.0100    0.0002
##    300        0.9721             nan     0.0100   -0.0005
##    320        0.9588             nan     0.0100   -0.0002
##    340        0.9458             nan     0.0100   -0.0002
##    360        0.9337             nan     0.0100   -0.0001
##    380        0.9220             nan     0.0100   -0.0001
##    400        0.9109             nan     0.0100   -0.0001
##    420        0.9003             nan     0.0100   -0.0004
##    440        0.8905             nan     0.0100   -0.0003
##    460        0.8810             nan     0.0100   -0.0004
##    480        0.8715             nan     0.0100   -0.0002
##    500        0.8623             nan     0.0100   -0.0000
##    520        0.8534             nan     0.0100   -0.0001
##    540        0.8450             nan     0.0100   -0.0002
##    560        0.8368             nan     0.0100   -0.0002
##    580        0.8290             nan     0.0100   -0.0001
##    600        0.8215             nan     0.0100   -0.0001
##    620        0.8135             nan     0.0100   -0.0001
##    640        0.8065             nan     0.0100   -0.0003
##    660        0.7991             nan     0.0100   -0.0003
##    680        0.7925             nan     0.0100   -0.0003
##    700        0.7856             nan     0.0100   -0.0005
##    720        0.7796             nan     0.0100   -0.0006
##    740        0.7733             nan     0.0100   -0.0006
##    760        0.7664             nan     0.0100   -0.0003
##    780        0.7601             nan     0.0100   -0.0002
##    800        0.7545             nan     0.0100   -0.0003
##    820        0.7487             nan     0.0100   -0.0003
##    840        0.7427             nan     0.0100   -0.0002
##    860        0.7367             nan     0.0100   -0.0004
##    880        0.7308             nan     0.0100   -0.0000
##    900        0.7254             nan     0.0100   -0.0001
##    920        0.7199             nan     0.0100   -0.0001
##    940        0.7144             nan     0.0100   -0.0002
##    960        0.7094             nan     0.0100   -0.0006
##    980        0.7039             nan     0.0100   -0.0002
##   1000        0.6990             nan     0.0100   -0.0003
# finding the best number of trees based on cross-validation
best_trees <- gbm.perf(gbm_model, method = "cv")

predictions_gbm <- predict(gbm_model, test_data, n.trees = best_trees)
mse_gbm <- mean((y_test - predictions_gbm)^2)
rmse_gbm <- sqrt(mse_gbm)

roc_gbm <- roc(y_test, predictions_gbm)
## Setting levels: control = -3.58, case = -2.22
## Setting direction: controls < cases
auc_gbm <- auc(roc_gbm)

cat("GBM Test MSE:", mse_gbm, "\n")
## GBM Test MSE: 1.123562
cat("GBM Test RMSE:", rmse_gbm, "\n")
## GBM Test RMSE: 1.059982
cat("GBM Test AUC:", auc_gbm, "\n")
## GBM Test AUC: 1
plot(roc_gbm, main = "ROC Curve (GBM)")

summary(gbm_model)

Cross-Validation

profvis({
  control <- trainControl(method = "cv", number = 5)

  # lasso with cross-validation
  fit_lasso_cv <- train(x_train, y_train, method = "glmnet", 
                        trControl = control, tuneGrid = expand.grid(alpha = 1, lambda = fit_lasso$lambda.min))
  print(fit_lasso_cv)
  
  # ridge with cross-validation
  fit_ridge_cv <- train(x_train, y_train, method = "glmnet", 
                        trControl = control, tuneGrid = expand.grid(alpha = 0, lambda = fit_ridge$lambda.min))
  print(fit_ridge_cv)
  
  # enet with cross-validation
  fit_enet_cv <- train(x_train, y_train, method = "glmnet", 
                       trControl = control, tuneGrid = expand.grid(alpha = 0.5, lambda = fit_enet$lambda.min))
  print(fit_enet_cv)
  
  # random forest with cross-validation
  rf_cv <- train(x_train, y_train, method = "rf", trControl = control)
  print(rf_cv)
  
  # GBM with cross-validation
  gbm_cv <- train(hs_zbmi_who ~ ., data = train_data, method = "gbm", trControl = control, verbose = FALSE)
  print(gbm_cv)
})
## glmnet 
## 
## 910 samples
##  61 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 729, 727, 728, 729, 727 
## Resampling results:
## 
##   RMSE      Rsquared   MAE      
##   1.054526  0.2325496  0.8371573
## 
## Tuning parameter 'alpha' was held constant at a value of 1
## Tuning
##  parameter 'lambda' was held constant at a value of 0.01696465
## glmnet 
## 
## 910 samples
##  61 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 728, 728, 728, 728, 728 
## Resampling results:
## 
##   RMSE      Rsquared   MAE      
##   1.069057  0.2090251  0.8468801
## 
## Tuning parameter 'alpha' was held constant at a value of 0
## Tuning
##  parameter 'lambda' was held constant at a value of 0.2578475
## glmnet 
## 
## 910 samples
##  61 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 728, 727, 729, 727, 729 
## Resampling results:
## 
##   RMSE      Rsquared   MAE      
##   1.074543  0.2018854  0.8459061
## 
## Tuning parameter 'alpha' was held constant at a value of 0.5
## Tuning
##  parameter 'lambda' was held constant at a value of 0.03091511
## Random Forest 
## 
## 910 samples
##  61 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 728, 727, 729, 728, 728 
## Resampling results across tuning parameters:
## 
##   mtry  RMSE      Rsquared   MAE      
##    2    1.112479  0.1884249  0.8811975
##   31    1.076084  0.1993703  0.8449897
##   61    1.075272  0.1985940  0.8456755
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 61.
## Stochastic Gradient Boosting 
## 
## 910 samples
##  37 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 728, 729, 727, 729, 727 
## Resampling results across tuning parameters:
## 
##   interaction.depth  n.trees  RMSE      Rsquared   MAE      
##   1                   50      1.100875  0.1650372  0.8698880
##   1                  100      1.082768  0.1886242  0.8554560
##   1                  150      1.080526  0.1944005  0.8540844
##   2                   50      1.089094  0.1795390  0.8580456
##   2                  100      1.091353  0.1826065  0.8627443
##   2                  150      1.101216  0.1771400  0.8735445
##   3                   50      1.076080  0.2027194  0.8526312
##   3                  100      1.086496  0.1927068  0.8616613
##   3                  150      1.101047  0.1811737  0.8709619
## 
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
## 
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were n.trees = 50, interaction.depth =
##  3, shrinkage = 0.1 and n.minobsinnode = 10.

With Metabolomic Serum Data

First 10 rows and columns of the metabolomic serum data

load("/Users/allison/Library/CloudStorage/GoogleDrive-aflouie@usc.edu/My Drive/HELIX_data/metabol_serum.RData")
kable(metabol_serum.d[1:10,1:10], align="c", digits=2, format="pipe")
430 1187 940 936 788 698 380 196 114 885
metab_1 -2.15 -0.69 -0.69 -0.19 -1.96 -1.90 -0.22 -1.38 -0.54 -1.25
metab_2 -0.71 -0.37 -0.36 -0.34 -0.35 -0.63 -0.26 -0.46 -0.44 -0.48
metab_3 8.60 9.15 8.95 8.54 8.73 8.24 9.03 8.29 8.37 8.18
metab_4 0.55 -1.33 -0.13 -0.62 -0.80 -0.46 0.49 0.12 -0.76 -0.07
metab_5 7.05 6.89 7.10 7.01 6.90 6.94 6.77 6.62 6.85 7.24
metab_6 5.79 5.81 5.86 5.95 5.95 5.42 5.82 5.65 5.44 5.60
metab_7 3.75 4.26 4.35 4.24 4.88 4.70 4.08 4.73 3.98 4.30
metab_8 5.07 5.08 5.92 5.41 5.39 4.62 5.10 5.28 4.51 5.45
metab_9 -1.87 -2.30 -1.97 -1.89 -1.55 -1.78 -2.29 -1.64 -2.02 -1.68
metab_10 -2.77 -3.42 -3.40 -2.84 -2.45 -3.14 -3.36 -2.88 -3.05 -2.92 
metabol_serum_transposed <- as.data.frame(t(metabol_serum.d))
metabol_serum_transposed$ID <- as.integer(rownames(metabol_serum_transposed))

# Add the ID column to the first position
metabol_serum_transposed <- metabol_serum_transposed[, c("ID", setdiff(names(metabol_serum_transposed), "ID"))]

# Now, the ID is the first column, and the layout is preserved
kable(head(metabol_serum_transposed), align = "c", digits = 2, format = "pipe")
ID metab_1 metab_2 metab_3 metab_4 metab_5 metab_6 metab_7 metab_8 metab_9 metab_10 metab_11 metab_12 metab_13 metab_14 metab_15 metab_16 metab_17 metab_18 metab_19 metab_20 metab_21 metab_22 metab_23 metab_24 metab_25 metab_26 metab_27 metab_28 metab_29 metab_30 metab_31 metab_32 metab_33 metab_34 metab_35 metab_36 metab_37 metab_38 metab_39 metab_40 metab_41 metab_42 metab_43 metab_44 metab_45 metab_46 metab_47 metab_48 metab_49 metab_50 metab_51 metab_52 metab_53 metab_54 metab_55 metab_56 metab_57 metab_58 metab_59 metab_60 metab_61 metab_62 metab_63 metab_64 metab_65 metab_66 metab_67 metab_68 metab_69 metab_70 metab_71 metab_72 metab_73 metab_74 metab_75 metab_76 metab_77 metab_78 metab_79 metab_80 metab_81 metab_82 metab_83 metab_84 metab_85 metab_86 metab_87 metab_88 metab_89 metab_90 metab_91 metab_92 metab_93 metab_94 metab_95 metab_96 metab_97 metab_98 metab_99 metab_100 metab_101 metab_102 metab_103 metab_104 metab_105 metab_106 metab_107 metab_108 metab_109 metab_110 metab_111 metab_112 metab_113 metab_114 metab_115 metab_116 metab_117 metab_118 metab_119 metab_120 metab_121 metab_122 metab_123 metab_124 metab_125 metab_126 metab_127 metab_128 metab_129 metab_130 metab_131 metab_132 metab_133 metab_134 metab_135 metab_136 metab_137 metab_138 metab_139 metab_140 metab_141 metab_142 metab_143 metab_144 metab_145 metab_146 metab_147 metab_148 metab_149 metab_150 metab_151 metab_152 metab_153 metab_154 metab_155 metab_156 metab_157 metab_158 metab_159 metab_160 metab_161 metab_162 metab_163 metab_164 metab_165 metab_166 metab_167 metab_168 metab_169 metab_170 metab_171 metab_172 metab_173 metab_174 metab_175 metab_176 metab_177
430 430 -2.15 -0.71 8.60 0.55 7.05 5.79 3.75 5.07 -1.87 -2.77 -3.31 -2.91 -2.94 -1.82 -4.40 -4.10 -5.41 -5.13 -5.35 -3.39 -5.08 -6.06 -6.06 -4.99 -4.46 -4.63 -3.27 -4.61 2.17 -1.73 -4.97 -4.90 -2.63 -5.29 -2.38 -4.06 -5.11 -5.35 -4.80 -3.92 -3.92 -5.47 -4.22 -2.56 -3.93 5.15 6.03 10.20 5.14 7.82 12.31 7.27 7.08 1.79 7.73 7.98 1.96 6.15 0.98 0.60 4.42 4.36 5.85 1.03 2.74 -2.53 -2.05 -2.91 -1.61 -1.63 5.03 0.14 6.23 -2.95 1.29 1.70 -2.83 4.55 4.05 2.56 -0.29 8.33 9.93 4.89 1.28 2.16 5.82 8.95 7.72 8.41 4.71 0.10 2.02 0.16 5.82 7.45 6.17 6.81 -0.70 -1.25 -0.65 2.05 3.39 4.94 -0.69 -1.44 -2.06 -2.44 -1.30 -0.73 -1.52 -2.43 -3.26 1.97 0.03 1.09 3.98 4.56 4.16 0.42 3.48 4.88 3.84 4.70 4.04 1.58 -0.76 1.75 2.48 4.43 4.68 3.29 0.97 1.03 0.44 1.55 2.26 2.72 0.12 -0.90 -0.50 0.02 -0.18 1.02 -2.69 -1.66 0.47 0.28 6.75 7.67 -2.66 -1.52 7.28 -0.08 2.39 1.55 3.01 2.92 -0.48 6.78 3.90 4.05 3.17 -1.46 3.56 4.60 -3.55 -2.79 -1.98 -1.84 3.98 6.47 7.16 -0.01 6.57 6.86 8.36
1187 1187 -0.69 -0.37 9.15 -1.33 6.89 5.81 4.26 5.08 -2.30 -3.42 -3.63 -3.16 -3.22 -1.57 -4.10 -5.35 -5.68 -6.11 -5.54 -3.50 -5.24 -5.72 -5.97 -4.94 -4.25 -4.46 -3.55 -4.64 1.81 -2.92 -4.44 -4.49 -3.53 -4.94 -3.15 -4.13 -4.47 -4.90 -4.24 -3.49 -3.94 -4.99 -4.02 -2.69 -3.69 5.13 5.57 9.93 6.13 8.47 12.32 6.83 5.94 1.64 6.82 7.74 1.98 6.11 0.99 0.19 4.34 4.36 5.47 0.92 2.69 -2.69 -1.93 -2.79 -1.63 -1.69 4.58 0.41 6.14 -3.06 1.05 2.10 -2.95 4.51 4.30 2.57 0.08 8.27 9.54 4.61 1.39 1.91 5.91 8.59 7.34 8.04 4.29 -0.04 2.17 0.42 5.39 6.95 5.68 6.09 -0.68 -1.29 -0.76 1.84 3.06 4.40 -0.52 -1.52 -1.90 -2.44 -1.46 -1.00 -1.33 -2.41 -3.67 2.48 0.27 1.02 4.19 4.43 4.19 0.33 3.24 4.38 3.92 5.09 4.42 1.01 -0.53 1.36 2.25 4.54 5.10 3.45 0.65 0.83 0.36 1.68 2.56 2.70 0.02 -1.02 -0.93 -0.22 0.11 1.60 -2.70 -1.31 1.08 0.54 6.29 7.97 -3.22 -1.34 7.50 0.48 2.19 1.49 3.09 2.71 -0.38 6.86 3.77 4.31 3.23 -1.82 3.80 5.05 -3.31 -2.18 -2.21 -2.01 4.91 6.84 7.14 0.14 6.03 6.55 7.91
940 940 -0.69 -0.36 8.95 -0.13 7.10 5.86 4.35 5.92 -1.97 -3.40 -3.41 -2.99 -3.01 -1.65 -3.55 -4.82 -5.41 -5.84 -5.13 -2.83 -4.86 -5.51 -5.51 -4.63 -3.73 -4.00 -2.92 -4.21 2.79 -1.41 -4.80 -5.47 -2.10 -5.47 -2.14 -4.18 -4.84 -5.24 -4.64 -3.20 -3.90 -5.24 -3.77 -2.70 -2.76 5.21 5.86 9.78 6.38 8.29 12.49 7.01 6.49 1.97 7.17 7.62 2.40 6.93 1.85 1.45 5.11 5.30 6.27 2.35 3.31 -2.50 -1.41 -2.61 -0.93 -1.03 4.54 1.59 6.03 -2.74 1.79 2.68 -8.16 5.19 5.14 3.16 0.24 9.09 10.25 5.44 1.90 2.46 6.66 9.19 8.24 8.46 5.73 1.10 2.58 1.15 6.37 7.28 6.51 7.20 -0.48 -0.69 -0.02 2.56 3.76 5.33 -0.16 -1.18 -1.18 -2.16 -1.06 -0.19 -0.48 -2.35 -3.16 2.79 0.72 2.14 4.80 4.84 4.55 1.27 4.26 5.23 4.40 5.43 4.56 2.32 0.03 2.15 3.22 5.06 5.28 3.80 1.38 1.58 0.98 2.27 2.94 3.39 0.33 -0.53 0.17 0.53 0.57 1.69 -2.21 -0.76 1.25 0.49 6.49 8.84 -4.02 -1.33 7.42 0.71 2.81 2.03 3.30 3.00 -0.24 7.02 3.82 4.66 3.36 -1.18 3.82 4.91 -2.95 -2.89 -2.43 -2.05 4.25 7.02 7.36 0.14 6.57 6.68 8.12
936 936 -0.19 -0.34 8.54 -0.62 7.01 5.95 4.24 5.41 -1.89 -2.84 -3.38 -3.11 -2.94 -1.45 -3.83 -4.43 -5.61 -5.41 -5.54 -2.94 -4.78 -6.06 -5.88 -4.70 -4.82 -4.46 -2.66 -3.82 2.85 -2.70 -5.16 -5.47 -3.31 -5.61 -2.80 -4.11 -4.97 -4.86 -5.01 -3.63 -3.78 -5.29 -4.17 -2.49 -3.65 5.31 5.60 9.87 6.67 8.05 12.33 6.72 6.42 1.25 7.28 7.37 1.99 6.28 1.17 0.50 4.52 4.43 5.54 1.30 3.08 -2.92 -2.16 -3.18 -1.66 -1.63 4.55 0.53 5.73 -3.27 1.30 1.70 -2.57 4.53 4.14 2.61 -0.18 8.32 9.62 4.82 1.58 1.99 5.82 8.59 7.58 8.39 4.68 0.36 2.01 -0.31 5.71 7.35 6.22 6.66 -0.70 -1.42 -0.62 2.13 3.54 4.85 -0.72 -1.53 -2.04 -2.37 -1.38 -0.96 -1.57 -2.91 -3.60 2.37 0.21 0.92 4.05 4.27 4.33 0.24 3.38 4.45 3.71 4.74 4.44 1.51 -1.73 1.51 2.27 4.37 4.89 3.40 0.66 0.83 0.27 1.50 2.30 2.60 0.14 -0.90 -0.99 -0.53 -0.30 1.14 -3.06 -1.69 0.39 0.19 6.21 8.05 -2.75 -0.87 7.79 0.87 2.48 1.62 3.28 2.93 -0.41 6.91 3.75 4.38 3.20 -1.07 3.81 4.89 -3.36 -2.40 -2.06 -2.03 3.99 7.36 6.94 0.14 6.26 6.47 7.98
788 788 -1.96 -0.35 8.73 -0.80 6.90 5.95 4.88 5.39 -1.55 -2.45 -3.51 -2.84 -2.83 -1.71 -3.91 -4.05 -5.61 -4.63 -5.29 -3.51 -4.86 -5.97 -5.27 -4.90 -4.40 -4.63 -3.11 -3.99 2.87 -2.23 -4.61 -5.04 -3.53 -5.08 -3.02 -4.41 -4.72 -5.18 -4.72 -3.63 -3.61 -5.29 -4.05 -2.31 -3.73 4.69 5.31 9.69 6.76 8.21 12.18 6.75 6.51 1.15 7.38 7.93 1.76 5.68 -0.02 -0.65 4.14 3.36 4.43 0.21 1.98 -2.31 -1.54 -2.30 -1.66 -1.47 4.48 0.88 6.47 -2.50 0.74 1.12 -2.17 4.31 3.50 2.09 -0.60 8.06 9.69 3.99 0.54 1.60 5.60 8.71 7.32 8.03 3.27 -0.98 1.59 -0.20 5.68 7.16 5.57 6.16 -0.79 -1.31 -0.87 2.17 3.23 4.57 -0.93 -1.80 -2.27 -2.51 -1.74 -1.02 -1.92 -2.02 -3.79 1.95 -0.24 0.40 3.73 4.13 3.71 0.03 2.89 4.06 3.54 4.76 3.88 0.53 -2.11 1.27 1.99 4.13 4.58 2.88 0.22 0.39 0.22 1.44 2.02 2.22 0.00 -0.81 -1.10 -0.41 -0.09 1.00 -2.66 -1.55 0.33 0.19 6.47 7.89 -4.40 -1.94 7.65 0.38 1.66 0.84 2.78 2.26 -0.84 6.52 3.53 3.81 2.83 -1.69 3.65 4.47 -3.81 -2.97 -2.88 -2.29 3.88 6.99 7.38 -0.10 6.00 6.52 8.04
698 698 -1.90 -0.63 8.24 -0.46 6.94 5.42 4.70 4.62 -1.78 -3.14 -3.46 -2.90 -2.94 -1.65 -4.20 -4.56 -5.68 -5.61 -5.41 -2.92 -5.04 -5.97 -6.06 -4.90 -4.22 -4.20 -3.05 -4.61 2.15 -2.87 -4.68 -5.08 -3.69 -5.24 -3.63 -4.24 -5.16 -5.35 -4.97 -3.61 -3.99 -5.35 -3.98 -2.59 -3.95 5.15 5.82 10.00 5.54 8.15 12.28 6.80 6.23 1.88 7.07 7.38 2.06 6.79 1.67 1.00 4.79 4.79 5.71 1.99 3.29 -2.13 -1.01 -1.85 -1.23 -0.90 4.41 -0.02 6.09 -2.10 1.66 2.27 -3.48 4.96 4.76 2.64 0.05 8.91 9.99 5.16 1.53 2.11 6.28 8.77 8.03 8.66 5.99 0.87 2.30 0.63 6.23 7.50 6.75 7.22 -0.45 -0.81 -0.11 2.57 3.93 5.16 -0.31 -1.19 -1.25 -1.93 -0.89 0.07 -0.87 -1.12 -3.03 2.61 0.54 1.83 4.50 4.53 4.42 1.15 4.02 4.91 4.06 5.06 4.42 2.02 -1.03 1.87 2.96 4.84 5.08 3.62 1.13 1.23 0.75 2.26 2.80 3.04 0.41 -0.39 0.02 0.31 0.52 1.73 -2.28 -0.73 1.06 0.72 6.44 7.27 -3.08 -1.23 7.35 0.92 2.60 2.00 3.69 3.20 -0.25 7.38 4.15 5.00 3.88 -1.39 4.31 5.20 -3.47 -2.75 -1.97 -1.96 4.18 6.81 6.75 0.02 6.49 5.97 7.78

LASSO

#removing any NA, might be problematic but hard to impute completely
selected_metabolomics_data <- selected_metabolomics_data %>% na.omit()

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[ trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who ~ ., train_data)[,-1]
y_train <- train_data$hs_zbmi_who
x_test <- model.matrix(hs_zbmi_who ~ ., test_data)[,-1]
y_test <- test_data$hs_zbmi_who

lasso_model <- cv.glmnet(x_train, y_train, alpha = 1, family = "gaussian")
plot(lasso_model)

lasso_model$lambda.min
## [1] 0.006317593
coef(lasso_model, s = lasso_model$lambda.min)
## 240 x 1 sparse Matrix of class "dgCMatrix"
##                                         s1
## (Intercept)                    9.652612753
## hs_child_age_None             -0.125015988
## h_cohort2                     -0.178612364
## h_cohort3                      0.239984197
## h_cohort4                      0.277482344
## h_cohort5                      .          
## h_cohort6                      0.076084251
## e3_sex_Nonemale                0.337746920
## e3_yearbir_None2004           -0.109978813
## e3_yearbir_None2005           -0.037950566
## e3_yearbir_None2006            0.041309884
## e3_yearbir_None2007            0.070061649
## e3_yearbir_None2008            .          
## e3_yearbir_None2009            0.440353330
## h_edumc_None2                  .          
## h_edumc_None3                  0.054730974
## h_native_None1                 .          
## h_native_None2                 0.030640414
## hs_cd_c_Log2                   0.004233189
## hs_co_c_Log2                   .          
## hs_cs_c_Log2                   0.106471288
## hs_cu_c_Log2                   0.161959408
## hs_hg_c_Log2                  -0.047861012
## hs_mo_c_Log2                  -0.047670350
## hs_pb_c_Log2                   .          
## hs_dde_cadj_Log2              -0.018322367
## hs_pcb153_cadj_Log2           -0.223070623
## hs_pcb170_cadj_Log2           -0.034259805
## hs_dep_cadj_Log2              -0.011178755
## hs_pbde153_cadj_Log2          -0.015997473
## hs_pfhxs_c_Log2                .          
## hs_pfoa_c_Log2                -0.031543757
## hs_pfos_c_Log2                 0.011634524
## hs_prpa_cadj_Log2             -0.009984648
## hs_mbzp_cadj_Log2              0.054349990
## hs_mibp_cadj_Log2              .          
## hs_mnbp_cadj_Log2             -0.001456852
## h_bfdur_Ter(10.8,34.9]         0.097697017
## h_bfdur_Ter(34.9,Inf]          0.123734223
## hs_bakery_prod_Ter(2,6]        0.018896136
## hs_bakery_prod_Ter(6,Inf]     -0.085793766
## hs_dairy_Ter(14.6,25.6]       -0.003998940
## hs_dairy_Ter(25.6,Inf]         0.072458675
## hs_fastfood_Ter(0.132,0.5]     .          
## hs_fastfood_Ter(0.5,Inf]      -0.020249340
## hs_org_food_Ter(0.132,1]       0.041429106
## hs_org_food_Ter(1,Inf]         0.018144596
## hs_readymade_Ter(0.132,0.5]    0.076617183
## hs_readymade_Ter(0.5,Inf]      0.052949999
## hs_total_bread_Ter(7,17.5]     .          
## hs_total_bread_Ter(17.5,Inf]   .          
## hs_total_fish_Ter(1.5,3]       .          
## hs_total_fish_Ter(3,Inf]      -0.046255786
## hs_total_fruits_Ter(7,14.1]    0.081684206
## hs_total_fruits_Ter(14.1,Inf]  0.127364350
## hs_total_lipids_Ter(3,7]       0.057620281
## hs_total_lipids_Ter(7,Inf]     .          
## hs_total_potatoes_Ter(3,4]     0.008046024
## hs_total_potatoes_Ter(4,Inf]   .          
## hs_total_sweets_Ter(4.1,8.5]   .          
## hs_total_sweets_Ter(8.5,Inf]   .          
## hs_total_veg_Ter(6,8.5]        0.026622043
## hs_total_veg_Ter(8.5,Inf]     -0.005827837
## metab_1                       -0.020785897
## metab_2                        0.073096038
## metab_3                        0.032034926
## metab_4                        0.003446253
## metab_5                        0.468786494
## metab_6                       -0.097649880
## metab_7                        .          
## metab_8                        0.217490779
## metab_9                        .          
## metab_10                       0.032087540
## metab_11                       0.184273933
## metab_12                      -0.149435967
## metab_13                       .          
## metab_14                      -0.434506087
## metab_15                       .          
## metab_16                       .          
## metab_17                      -0.007565700
## metab_18                      -0.186515334
## metab_19                       .          
## metab_20                       .          
## metab_21                       0.027549314
## metab_22                      -0.244341002
## metab_23                       0.146432710
## metab_24                       0.632567367
## metab_25                      -0.130026099
## metab_26                      -0.237944780
## metab_27                       0.521933363
## metab_28                       .          
## metab_29                      -0.019989581
## metab_30                       0.153011592
## metab_31                       0.053300669
## metab_32                      -0.142487713
## metab_33                       .          
## metab_34                      -0.011121071
## metab_35                       .          
## metab_36                       .          
## metab_37                      -0.035444486
## metab_38                      -0.053022833
## metab_39                      -0.003334899
## metab_40                       0.044520450
## metab_41                       0.249852509
## metab_42                      -0.405907450
## metab_43                      -0.158581284
## metab_44                      -0.045288800
## metab_45                       0.130376443
## metab_46                       .          
## metab_47                       0.457616223
## metab_48                      -0.783285866
## metab_49                       0.117109155
## metab_50                      -0.188337510
## metab_51                       .          
## metab_52                       0.443884351
## metab_53                       .          
## metab_54                       0.121219769
## metab_55                       .          
## metab_56                      -0.136020552
## metab_57                       .          
## metab_58                       .          
## metab_59                       0.603780730
## metab_60                      -0.154424356
## metab_61                       .          
## metab_62                       .          
## metab_63                      -0.161019814
## metab_64                       .          
## metab_65                       .          
## metab_66                      -0.084873517
## metab_67                      -0.263063976
## metab_68                       0.137153805
## metab_69                      -0.067164949
## metab_70                       .          
## metab_71                      -0.066501000
## metab_72                       .          
## metab_73                      -0.123044461
## metab_74                       .          
## metab_75                       0.305359360
## metab_76                       .          
## metab_77                       0.013700114
## metab_78                      -0.127952913
## metab_79                       .          
## metab_80                       .          
## metab_81                       .          
## metab_82                      -0.658204717
## metab_83                       .          
## metab_84                      -0.099522817
## metab_85                       .          
## metab_86                       0.377147684
## metab_87                       0.050659558
## metab_88                       0.627678593
## metab_89                      -1.326499919
## metab_90                       .          
## metab_91                       0.135298705
## metab_92                       0.104189432
## metab_93                       .          
## metab_94                      -0.058806180
## metab_95                       1.648017671
## metab_96                       0.013536044
## metab_97                       .          
## metab_98                       .          
## metab_99                      -0.471488065
## metab_100                      0.600253840
## metab_101                      .          
## metab_102                      .          
## metab_103                     -0.465663773
## metab_104                      0.142828557
## metab_105                      0.137140807
## metab_106                      0.103884323
## metab_107                      0.049901842
## metab_108                      .          
## metab_109                     -0.260892420
## metab_110                     -0.165457401
## metab_111                      .          
## metab_112                      .          
## metab_113                      0.659426190
## metab_114                      .          
## metab_115                      0.525579174
## metab_116                      .          
## metab_117                      .          
## metab_118                     -0.372785082
## metab_119                      .          
## metab_120                     -0.263488288
## metab_121                      .          
## metab_122                      .          
## metab_123                      .          
## metab_124                      .          
## metab_125                     -0.191346026
## metab_126                      .          
## metab_127                     -0.023853642
## metab_128                     -0.001830550
## metab_129                      .          
## metab_130                      .          
## metab_131                      .          
## metab_132                      .          
## metab_133                     -0.294838104
## metab_134                      0.359310084
## metab_135                     -0.264462850
## metab_136                      .          
## metab_137                     -0.389533069
## metab_138                     -0.523098646
## metab_139                      .          
## metab_140                     -0.002059593
## metab_141                      .          
## metab_142                     -0.621749560
## metab_143                     -0.267165989
## metab_144                      0.014590054
## metab_145                     -0.191413185
## metab_146                     -0.007204806
## metab_147                      0.547810987
## metab_148                      .          
## metab_149                      .          
## metab_150                      0.277334322
## metab_151                     -0.005555498
## metab_152                     -0.046231938
## metab_153                      .          
## metab_154                     -0.017119716
## metab_155                     -0.374027935
## metab_156                      .          
## metab_157                      0.201783156
## metab_158                      .          
## metab_159                      0.131018354
## metab_160                     -2.124408269
## metab_161                      2.446554446
## metab_162                      .          
## metab_163                      0.597766767
## metab_164                     -0.089949931
## metab_165                      .          
## metab_166                     -0.387780142
## metab_167                     -0.090688458
## metab_168                     -0.008939408
## metab_169                      .          
## metab_170                      .          
## metab_171                     -0.084162368
## metab_172                      .          
## metab_173                      0.065001642
## metab_174                      .          
## metab_175                     -0.222972504
## metab_176                     -0.061410628
## metab_177                      0.137079628
lasso_predictions <- predict(lasso_model, s = lasso_model$lambda.min, newx = x_test)

test_mse <- mean((lasso_predictions - y_test)^2)
cat("Mean Squared Error on Test Set:", test_mse, "\n")
## Mean Squared Error on Test Set: 0.7397599
# convert hs_zbmi_who to binary based on median
median_value <- median(selected_metabolomics_data$hs_zbmi_who, na.rm = TRUE)
selected_metabolomics_data$hs_zbmi_who_binary <- ifelse(selected_metabolomics_data$hs_zbmi_who > median_value, 1, 0)

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who_binary, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, train_data)[,-1]
y_train <- train_data$hs_zbmi_who_binary
x_test <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, test_data)[,-1]
y_test <- test_data$hs_zbmi_who_binary

# fit LASSO model using cross-validation
lasso_model <- cv.glmnet(x_train, y_train, alpha = 1, family = "binomial")
plot(lasso_model)

best_lambda <- lasso_model$lambda.min
cat("Best Lambda:", best_lambda, "\n")
## Best Lambda: 0.01054902
# Get coefficients at best lambda
coef(lasso_model, s = best_lambda)
## 240 x 1 sparse Matrix of class "dgCMatrix"
##                                          s1
## (Intercept)                    7.937250e+00
## hs_child_age_None             -7.322684e-02
## h_cohort2                     -3.980672e-01
## h_cohort3                      .           
## h_cohort4                      .           
## h_cohort5                      .           
## h_cohort6                      .           
## e3_sex_Nonemale                2.057458e-01
## e3_yearbir_None2004           -3.259318e-01
## e3_yearbir_None2005           -2.010076e-02
## e3_yearbir_None2006            5.158542e-02
## e3_yearbir_None2007            .           
## e3_yearbir_None2008            .           
## e3_yearbir_None2009            8.923769e-01
## h_edumc_None2                  4.762899e-02
## h_edumc_None3                  .           
## h_native_None1                 .           
## h_native_None2                 4.570936e-01
## hs_cd_c_Log2                   .           
## hs_co_c_Log2                   .           
## hs_cs_c_Log2                   1.236241e-02
## hs_cu_c_Log2                   .           
## hs_hg_c_Log2                   .           
## hs_mo_c_Log2                  -2.580655e-02
## hs_pb_c_Log2                   .           
## hs_dde_cadj_Log2               .           
## hs_pcb153_cadj_Log2           -3.012537e-01
## hs_pcb170_cadj_Log2           -1.658879e-02
## hs_dep_cadj_Log2              -2.149976e-02
## hs_pbde153_cadj_Log2          -4.576825e-02
## hs_pfhxs_c_Log2                .           
## hs_pfoa_c_Log2                -2.656628e-01
## hs_pfos_c_Log2                 .           
## hs_prpa_cadj_Log2              .           
## hs_mbzp_cadj_Log2              8.874895e-05
## hs_mibp_cadj_Log2              .           
## hs_mnbp_cadj_Log2              .           
## h_bfdur_Ter(10.8,34.9]         7.954782e-02
## h_bfdur_Ter(34.9,Inf]          .           
## hs_bakery_prod_Ter(2,6]        .           
## hs_bakery_prod_Ter(6,Inf]     -2.924093e-01
## hs_dairy_Ter(14.6,25.6]        .           
## hs_dairy_Ter(25.6,Inf]         .           
## hs_fastfood_Ter(0.132,0.5]     .           
## hs_fastfood_Ter(0.5,Inf]       .           
## hs_org_food_Ter(0.132,1]       2.613185e-02
## hs_org_food_Ter(1,Inf]         4.987130e-02
## hs_readymade_Ter(0.132,0.5]    .           
## hs_readymade_Ter(0.5,Inf]      .           
## hs_total_bread_Ter(7,17.5]     .           
## hs_total_bread_Ter(17.5,Inf]   .           
## hs_total_fish_Ter(1.5,3]       .           
## hs_total_fish_Ter(3,Inf]       .           
## hs_total_fruits_Ter(7,14.1]    .           
## hs_total_fruits_Ter(14.1,Inf]  4.616319e-02
## hs_total_lipids_Ter(3,7]       .           
## hs_total_lipids_Ter(7,Inf]     .           
## hs_total_potatoes_Ter(3,4]     1.760234e-05
## hs_total_potatoes_Ter(4,Inf]  -7.838245e-02
## hs_total_sweets_Ter(4.1,8.5]   .           
## hs_total_sweets_Ter(8.5,Inf]   .           
## hs_total_veg_Ter(6,8.5]        9.408405e-02
## hs_total_veg_Ter(8.5,Inf]     -9.448408e-02
## metab_1                        .           
## metab_2                        .           
## metab_3                        .           
## metab_4                        1.181569e-01
## metab_5                        8.504437e-01
## metab_6                        .           
## metab_7                        .           
## metab_8                        1.625507e-01
## metab_9                        .           
## metab_10                       .           
## metab_11                       .           
## metab_12                       .           
## metab_13                       .           
## metab_14                       .           
## metab_15                       .           
## metab_16                       .           
## metab_17                       .           
## metab_18                       .           
## metab_19                       .           
## metab_20                       .           
## metab_21                       .           
## metab_22                       .           
## metab_23                       4.888186e-02
## metab_24                       1.279110e-01
## metab_25                       .           
## metab_26                      -3.322651e-01
## metab_27                       .           
## metab_28                       3.260778e-01
## metab_29                       .           
## metab_30                       9.491181e-02
## metab_31                       .           
## metab_32                       .           
## metab_33                       .           
## metab_34                       .           
## metab_35                       .           
## metab_36                       5.262996e-01
## metab_37                      -9.104158e-02
## metab_38                      -3.164769e-01
## metab_39                      -4.299547e-03
## metab_40                       .           
## metab_41                       .           
## metab_42                       .           
## metab_43                       .           
## metab_44                       .           
## metab_45                       .           
## metab_46                      -6.087660e-02
## metab_47                       4.005154e-01
## metab_48                      -8.718817e-01
## metab_49                       8.155354e-01
## metab_50                      -2.389608e-01
## metab_51                       .           
## metab_52                       .           
## metab_53                       .           
## metab_54                       1.520904e-03
## metab_55                       .           
## metab_56                       .           
## metab_57                       .           
## metab_58                       .           
## metab_59                       2.708218e-01
## metab_60                       .           
## metab_61                       .           
## metab_62                       .           
## metab_63                       .           
## metab_64                       .           
## metab_65                       2.117688e-02
## metab_66                       .           
## metab_67                       .           
## metab_68                       .           
## metab_69                       .           
## metab_70                       .           
## metab_71                      -3.137810e-01
## metab_72                       .           
## metab_73                       .           
## metab_74                       .           
## metab_75                       .           
## metab_76                       .           
## metab_77                       .           
## metab_78                       .           
## metab_79                       .           
## metab_80                       .           
## metab_81                       6.815883e-01
## metab_82                      -1.178690e+00
## metab_83                       .           
## metab_84                       .           
## metab_85                       .           
## metab_86                       .           
## metab_87                       .           
## metab_88                       .           
## metab_89                       .           
## metab_90                       .           
## metab_91                       .           
## metab_92                       .           
## metab_93                       .           
## metab_94                       .           
## metab_95                       1.888814e+00
## metab_96                       .           
## metab_97                       .           
## metab_98                       .           
## metab_99                       .           
## metab_100                      .           
## metab_101                      .           
## metab_102                      .           
## metab_103                      .           
## metab_104                      3.133895e-01
## metab_105                      .           
## metab_106                      .           
## metab_107                      .           
## metab_108                      .           
## metab_109                      .           
## metab_110                      .           
## metab_111                      .           
## metab_112                      .           
## metab_113                      4.514091e-01
## metab_114                      .           
## metab_115                      1.881794e-01
## metab_116                     -2.287344e-02
## metab_117                      .           
## metab_118                     -1.045499e+00
## metab_119                      .           
## metab_120                     -4.159841e-02
## metab_121                      .           
## metab_122                     -7.894047e-01
## metab_123                     -1.010749e-02
## metab_124                      .           
## metab_125                      .           
## metab_126                      .           
## metab_127                     -1.481293e-01
## metab_128                      .           
## metab_129                      .           
## metab_130                      .           
## metab_131                      .           
## metab_132                      .           
## metab_133                     -6.203186e-01
## metab_134                      .           
## metab_135                      .           
## metab_136                      .           
## metab_137                      .           
## metab_138                      .           
## metab_139                      .           
## metab_140                      .           
## metab_141                      .           
## metab_142                     -8.472082e-02
## metab_143                      .           
## metab_144                      .           
## metab_145                     -5.315799e-01
## metab_146                     -1.384647e-01
## metab_147                      .           
## metab_148                      .           
## metab_149                      .           
## metab_150                      .           
## metab_151                      6.612960e-02
## metab_152                     -7.002718e-02
## metab_153                      .           
## metab_154                      .           
## metab_155                      .           
## metab_156                      .           
## metab_157                      .           
## metab_158                      .           
## metab_159                      .           
## metab_160                     -2.797393e+00
## metab_161                      3.983119e+00
## metab_162                      .           
## metab_163                      2.278074e-02
## metab_164                      .           
## metab_165                      .           
## metab_166                      .           
## metab_167                      .           
## metab_168                      .           
## metab_169                      .           
## metab_170                     -1.286578e-01
## metab_171                      .           
## metab_172                     -3.563937e-01
## metab_173                      6.535921e-01
## metab_174                      .           
## metab_175                      .           
## metab_176                      .           
## metab_177                      1.311648e-02
lasso_predictions <- predict(lasso_model, s = best_lambda, newx = x_test, type = "response")

# convert probabilities to binary predictions
binary_predictions <- ifelse(lasso_predictions > 0.5, 1, 0)

# make sure levels match between binary_predictions and y_test
binary_predictions <- factor(binary_predictions, levels = c(0, 1))
y_test <- factor(y_test, levels = c(0, 1))

# evaluate accuracy
accuracy <- mean(binary_predictions == y_test)
cat("LASSO Accuracy on Test Set:", accuracy, "\n")
## LASSO Accuracy on Test Set: 0.7402235
conf_matrix <- confusionMatrix(binary_predictions, y_test)
conf_matrix
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 133  47
##          1  46 132
##                                           
##                Accuracy : 0.7402          
##                  95% CI : (0.6915, 0.7849)
##     No Information Rate : 0.5             
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.4804          
##                                           
##  Mcnemar's Test P-Value : 1               
##                                           
##             Sensitivity : 0.7430          
##             Specificity : 0.7374          
##          Pos Pred Value : 0.7389          
##          Neg Pred Value : 0.7416          
##              Prevalence : 0.5000          
##          Detection Rate : 0.3715          
##    Detection Prevalence : 0.5028          
##       Balanced Accuracy : 0.7402          
##                                           
##        'Positive' Class : 0               
## 
# ROC Curve and AUC
roc_curve <- roc(as.numeric(y_test), as.numeric(lasso_predictions))
## Setting levels: control = 1, case = 2
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for LASSO Model")

auc_value <- auc(roc_curve)
cat("LASSO AUC on Test Set:", auc_value, "\n")
## LASSO AUC on Test Set: 0.8037827

Ridge

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[ trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who ~ . - hs_zbmi_who_binary, train_data)[,-1]
y_train <- train_data$hs_zbmi_who
x_test <- model.matrix(hs_zbmi_who ~ . - hs_zbmi_who_binary, test_data)[,-1]
y_test <- test_data$hs_zbmi_who

ridge_model <- cv.glmnet(x_train, y_train, alpha = 0, family = "gaussian")
plot(ridge_model)

ridge_model$lambda.min
## [1] 0.1053838
coef(ridge_model, s = ridge_model$lambda.min)
## 240 x 1 sparse Matrix of class "dgCMatrix"
##                                          s1
## (Intercept)                    2.4494205140
## hs_child_age_None             -0.0807562390
## h_cohort2                     -0.2322533256
## h_cohort3                      0.2148947058
## h_cohort4                      0.2742479627
## h_cohort5                      0.0305044324
## h_cohort6                      0.1345792853
## e3_sex_Nonemale                0.2762535283
## e3_yearbir_None2004           -0.1307669542
## e3_yearbir_None2005           -0.0662549700
## e3_yearbir_None2006            0.0488073797
## e3_yearbir_None2007            0.0874472743
## e3_yearbir_None2008            0.0140599433
## e3_yearbir_None2009            0.5262950664
## h_edumc_None2                  0.0209774799
## h_edumc_None3                  0.0770561650
## h_native_None1                -0.0103178724
## h_native_None2                 0.0699425628
## hs_cd_c_Log2                   0.0077592299
## hs_co_c_Log2                   0.0051414013
## hs_cs_c_Log2                   0.1047753386
## hs_cu_c_Log2                   0.2188135066
## hs_hg_c_Log2                  -0.0503031779
## hs_mo_c_Log2                  -0.0538732196
## hs_pb_c_Log2                  -0.0140226284
## hs_dde_cadj_Log2              -0.0356320943
## hs_pcb153_cadj_Log2           -0.1979003596
## hs_pcb170_cadj_Log2           -0.0399381366
## hs_dep_cadj_Log2              -0.0117487705
## hs_pbde153_cadj_Log2          -0.0168898180
## hs_pfhxs_c_Log2                0.0087279115
## hs_pfoa_c_Log2                -0.0551506976
## hs_pfos_c_Log2                 0.0119391752
## hs_prpa_cadj_Log2             -0.0087934187
## hs_mbzp_cadj_Log2              0.0525129143
## hs_mibp_cadj_Log2              0.0065806367
## hs_mnbp_cadj_Log2             -0.0185313521
## h_bfdur_Ter(10.8,34.9]         0.1157904148
## h_bfdur_Ter(34.9,Inf]          0.1561869467
## hs_bakery_prod_Ter(2,6]        0.0287020411
## hs_bakery_prod_Ter(6,Inf]     -0.0989934167
## hs_dairy_Ter(14.6,25.6]       -0.0278652010
## hs_dairy_Ter(25.6,Inf]         0.0701097207
## hs_fastfood_Ter(0.132,0.5]    -0.0212141982
## hs_fastfood_Ter(0.5,Inf]      -0.0455694841
## hs_org_food_Ter(0.132,1]       0.0479111617
## hs_org_food_Ter(1,Inf]         0.0297347170
## hs_readymade_Ter(0.132,0.5]    0.1098733269
## hs_readymade_Ter(0.5,Inf]      0.0781587855
## hs_total_bread_Ter(7,17.5]    -0.0161375308
## hs_total_bread_Ter(17.5,Inf]  -0.0141217088
## hs_total_fish_Ter(1.5,3]      -0.0227684885
## hs_total_fish_Ter(3,Inf]      -0.0576500860
## hs_total_fruits_Ter(7,14.1]    0.1097538366
## hs_total_fruits_Ter(14.1,Inf]  0.1423782091
## hs_total_lipids_Ter(3,7]       0.0867512469
## hs_total_lipids_Ter(7,Inf]     0.0164799505
## hs_total_potatoes_Ter(3,4]     0.0282635691
## hs_total_potatoes_Ter(4,Inf]   0.0082718606
## hs_total_sweets_Ter(4.1,8.5]  -0.0176421543
## hs_total_sweets_Ter(8.5,Inf]  -0.0043193424
## hs_total_veg_Ter(6,8.5]        0.0329623256
## hs_total_veg_Ter(8.5,Inf]     -0.0201305477
## metab_1                       -0.0356324575
## metab_2                        0.3093081048
## metab_3                        0.1068203955
## metab_4                        0.0198384064
## metab_5                        0.4048546629
## metab_6                       -0.1683142152
## metab_7                        0.0756138627
## metab_8                        0.3457958796
## metab_9                       -0.0511431874
## metab_10                       0.0750736543
## metab_11                       0.1801856557
## metab_12                      -0.1297303683
## metab_13                      -0.0398107305
## metab_14                      -0.5140013662
## metab_15                      -0.0160423797
## metab_16                       0.0319625514
## metab_17                      -0.0438826380
## metab_18                      -0.1818246007
## metab_19                      -0.0629747201
## metab_20                       0.0313230948
## metab_21                       0.2557173994
## metab_22                      -0.2593831265
## metab_23                       0.1489300876
## metab_24                       0.6589167008
## metab_25                      -0.1425958734
## metab_26                      -0.2566960932
## metab_27                       0.3825491134
## metab_28                       0.0619920398
## metab_29                      -0.0986542491
## metab_30                       0.1333568559
## metab_31                       0.0673468991
## metab_32                      -0.1394744288
## metab_33                       0.0147626931
## metab_34                      -0.0619354942
## metab_35                      -0.0280958420
## metab_36                      -0.0290727624
## metab_37                      -0.0955180595
## metab_38                      -0.0532691604
## metab_39                      -0.0104293549
## metab_40                       0.3513759032
## metab_41                       0.2664273334
## metab_42                      -0.4284613382
## metab_43                      -0.1853713484
## metab_44                      -0.1136538680
## metab_45                       0.1802531706
## metab_46                      -0.0625154848
## metab_47                       0.4363898328
## metab_48                      -0.6412412908
## metab_49                       0.1311827280
## metab_50                      -0.2540788244
## metab_51                       0.0342328965
## metab_52                       0.5012879046
## metab_53                       0.0468728997
## metab_54                       0.1158494094
## metab_55                       0.0123602953
## metab_56                      -0.1924275322
## metab_57                       0.0417974880
## metab_58                      -0.1537668957
## metab_59                       0.4846343980
## metab_60                      -0.1542577290
## metab_61                       0.0953787222
## metab_62                      -0.0471840293
## metab_63                      -0.1382679312
## metab_64                       0.0530170053
## metab_65                       0.0204393397
## metab_66                      -0.1330236555
## metab_67                      -0.1403191179
## metab_68                       0.1283040339
## metab_69                      -0.0866717093
## metab_70                      -0.0490907794
## metab_71                      -0.1250459783
## metab_72                      -0.0274823801
## metab_73                      -0.1219595478
## metab_74                       0.0329537071
## metab_75                       0.3019373615
## metab_76                      -0.0260404206
## metab_77                       0.0094595840
## metab_78                      -0.2759417047
## metab_79                       0.0162114356
## metab_80                       0.0406970885
## metab_81                       0.1374685570
## metab_82                      -0.4606395602
## metab_83                      -0.0960320149
## metab_84                      -0.1839203868
## metab_85                      -0.0182163420
## metab_86                       0.3022951567
## metab_87                       0.1261314125
## metab_88                       0.4018965809
## metab_89                      -0.4060073888
## metab_90                      -0.0491506273
## metab_91                       0.1519519407
## metab_92                       0.1169152959
## metab_93                      -0.0240086358
## metab_94                      -0.0807376606
## metab_95                       0.8113455686
## metab_96                       0.3362727238
## metab_97                      -0.1870766929
## metab_98                      -0.0494372877
## metab_99                      -0.4833755828
## metab_100                      0.4310798058
## metab_101                      0.1084737388
## metab_102                      0.0601884712
## metab_103                     -0.2634210926
## metab_104                      0.2157663551
## metab_105                      0.1381333203
## metab_106                      0.1075218916
## metab_107                      0.1282239294
## metab_108                     -0.0008768251
## metab_109                     -0.1914029546
## metab_110                     -0.2475460177
## metab_111                     -0.0943473483
## metab_112                      0.0559648830
## metab_113                      0.5506388048
## metab_114                      0.0589562048
## metab_115                      0.4357448367
## metab_116                      0.0502224951
## metab_117                     -0.1797498640
## metab_118                     -0.1849170592
## metab_119                      0.1100270441
## metab_120                     -0.3318540971
## metab_121                      0.1132077882
## metab_122                     -0.2645520339
## metab_123                     -0.1204987031
## metab_124                      0.0500019849
## metab_125                     -0.2439620063
## metab_126                      0.0254666574
## metab_127                     -0.0266735077
## metab_128                     -0.0769171410
## metab_129                      0.1023250491
## metab_130                     -0.1710254468
## metab_131                     -0.0242519209
## metab_132                      0.0352952669
## metab_133                     -0.2934894625
## metab_134                      0.2500414946
## metab_135                     -0.1544992765
## metab_136                     -0.1803280878
## metab_137                     -0.3504019669
## metab_138                     -0.3525008089
## metab_139                     -0.0266390329
## metab_140                     -0.0846205257
## metab_141                     -0.0803517507
## metab_142                     -0.3691865186
## metab_143                     -0.2479707334
## metab_144                      0.1602881185
## metab_145                     -0.2560717174
## metab_146                     -0.0366559517
## metab_147                      0.3502054310
## metab_148                      0.0402649223
## metab_149                      0.0504084491
## metab_150                      0.2507921258
## metab_151                      0.0070653444
## metab_152                     -0.0520637190
## metab_153                     -0.0470324841
## metab_154                     -0.0285517715
## metab_155                     -0.2948219993
## metab_156                     -0.0657415551
## metab_157                      0.1562791906
## metab_158                      0.1390909401
## metab_159                      0.2112649535
## metab_160                     -1.0462789923
## metab_161                      1.4450351855
## metab_162                     -0.0291513560
## metab_163                      0.7390823658
## metab_164                     -0.1151060261
## metab_165                     -0.0370357382
## metab_166                     -0.3800799041
## metab_167                     -0.1098805922
## metab_168                     -0.0706141033
## metab_169                      0.0280169693
## metab_170                     -0.0071393153
## metab_171                     -0.0617738843
## metab_172                     -0.0299629702
## metab_173                      0.1259658477
## metab_174                     -0.0806184771
## metab_175                     -0.2089224854
## metab_176                     -0.0844220296
## metab_177                      0.1678561164
predictions <- predict(ridge_model, s = ridge_model$lambda.min, newx = x_test)

test_mse <- mean((predictions - y_test)^2)
cat("Mean Squared Error on Test Set:", test_mse, "\n")
## Mean Squared Error on Test Set: 0.731053
# convert hs_zbmi_who to binary based on median
median_value <- median(selected_metabolomics_data$hs_zbmi_who, na.rm = TRUE)
selected_metabolomics_data$hs_zbmi_who_binary <- ifelse(selected_metabolomics_data$hs_zbmi_who > median_value, 1, 0)

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who_binary, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, train_data)[,-1]
y_train <- train_data$hs_zbmi_who_binary
x_test <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, test_data)[,-1]
y_test <- test_data$hs_zbmi_who_binary

# fit ridge model using cross-validation
ridge_model <- cv.glmnet(x_train, y_train, alpha = 0, family = "binomial")
plot(ridge_model)

best_lambda <- ridge_model$lambda.min
cat("Best Lambda:", best_lambda, "\n")
## Best Lambda: 0.09175002
coef(ridge_model, s = best_lambda)
## 240 x 1 sparse Matrix of class "dgCMatrix"
##                                          s1
## (Intercept)                   -3.1290728529
## hs_child_age_None             -0.0586481056
## h_cohort2                     -0.2663041638
## h_cohort3                      0.1435932560
## h_cohort4                      0.1969858711
## h_cohort5                      0.1158459554
## h_cohort6                      0.1780244278
## e3_sex_Nonemale                0.1230039748
## e3_yearbir_None2004           -0.3124975610
## e3_yearbir_None2005           -0.0944057219
## e3_yearbir_None2006            0.0559329921
## e3_yearbir_None2007            0.1043983171
## e3_yearbir_None2008            0.0964413750
## e3_yearbir_None2009            0.9837058948
## h_edumc_None2                  0.1641793864
## h_edumc_None3                  0.0830119438
## h_native_None1                 0.0004119497
## h_native_None2                 0.3150207915
## hs_cd_c_Log2                  -0.0195166972
## hs_co_c_Log2                   0.0801221848
## hs_cs_c_Log2                   0.1054396159
## hs_cu_c_Log2                   0.1705679267
## hs_hg_c_Log2                  -0.0161756218
## hs_mo_c_Log2                  -0.0754056982
## hs_pb_c_Log2                  -0.0410281648
## hs_dde_cadj_Log2              -0.0583766290
## hs_pcb153_cadj_Log2           -0.2217363771
## hs_pcb170_cadj_Log2           -0.0375230172
## hs_dep_cadj_Log2              -0.0248423449
## hs_pbde153_cadj_Log2          -0.0388870871
## hs_pfhxs_c_Log2                0.0180825617
## hs_pfoa_c_Log2                -0.2412180321
## hs_pfos_c_Log2                -0.0165278019
## hs_prpa_cadj_Log2              0.0008529876
## hs_mbzp_cadj_Log2              0.0383964223
## hs_mibp_cadj_Log2             -0.0095597323
## hs_mnbp_cadj_Log2             -0.0570776451
## h_bfdur_Ter(10.8,34.9]         0.1769788276
## h_bfdur_Ter(34.9,Inf]          0.1206273136
## hs_bakery_prod_Ter(2,6]        0.0017410711
## hs_bakery_prod_Ter(6,Inf]     -0.2612067971
## hs_dairy_Ter(14.6,25.6]       -0.0123591313
## hs_dairy_Ter(25.6,Inf]        -0.0174048131
## hs_fastfood_Ter(0.132,0.5]    -0.0947679355
## hs_fastfood_Ter(0.5,Inf]      -0.0549241633
## hs_org_food_Ter(0.132,1]       0.1136167763
## hs_org_food_Ter(1,Inf]         0.1682163295
## hs_readymade_Ter(0.132,0.5]    0.1215917587
## hs_readymade_Ter(0.5,Inf]      0.0535259119
## hs_total_bread_Ter(7,17.5]    -0.1214821627
## hs_total_bread_Ter(17.5,Inf]  -0.0634722347
## hs_total_fish_Ter(1.5,3]      -0.0053614464
## hs_total_fish_Ter(3,Inf]      -0.0380008278
## hs_total_fruits_Ter(7,14.1]    0.0231411035
## hs_total_fruits_Ter(14.1,Inf]  0.1231840389
## hs_total_lipids_Ter(3,7]       0.0301494359
## hs_total_lipids_Ter(7,Inf]    -0.0229767438
## hs_total_potatoes_Ter(3,4]     0.0385652000
## hs_total_potatoes_Ter(4,Inf]  -0.0908046511
## hs_total_sweets_Ter(4.1,8.5]   0.0495514872
## hs_total_sweets_Ter(8.5,Inf]   0.0499303412
## hs_total_veg_Ter(6,8.5]        0.1405000191
## hs_total_veg_Ter(8.5,Inf]     -0.1473289785
## metab_1                        0.0115176602
## metab_2                        0.2861279889
## metab_3                        0.0833757200
## metab_4                        0.0833701720
## metab_5                        0.5884114064
## metab_6                       -0.1674709537
## metab_7                        0.0762856038
## metab_8                        0.4063369557
## metab_9                       -0.1142505123
## metab_10                       0.1093658778
## metab_11                      -0.1747928560
## metab_12                      -0.1546406451
## metab_13                      -0.0549921435
## metab_14                      -0.0869963107
## metab_15                       0.0232990794
## metab_16                       0.0819369516
## metab_17                      -0.1240927578
## metab_18                      -0.0090787386
## metab_19                       0.0060151461
## metab_20                      -0.0749172082
## metab_21                       0.2448413297
## metab_22                      -0.1869099173
## metab_23                       0.2173737052
## metab_24                       0.5717082444
## metab_25                       0.0107053835
## metab_26                      -0.2987322578
## metab_27                       0.1399967511
## metab_28                       0.3576024408
## metab_29                      -0.0776832275
## metab_30                       0.1872533756
## metab_31                       0.0117049438
## metab_32                      -0.0852185808
## metab_33                      -0.0449736726
## metab_34                       0.0795776267
## metab_35                      -0.0603628939
## metab_36                       0.4117549638
## metab_37                      -0.1837769377
## metab_38                      -0.2864884780
## metab_39                      -0.1685351453
## metab_40                       0.4079876970
## metab_41                       0.1611417732
## metab_42                      -0.1917172916
## metab_43                      -0.2126068236
## metab_44                      -0.0888143608
## metab_45                       0.0454526136
## metab_46                      -0.2358128748
## metab_47                       0.4284773612
## metab_48                      -0.7091955362
## metab_49                       0.4912595738
## metab_50                      -0.3074575509
## metab_51                       0.2457988608
## metab_52                       0.3510731351
## metab_53                       0.1284500656
## metab_54                       0.2649541314
## metab_55                       0.1060371324
## metab_56                      -0.1037894614
## metab_57                       0.2087599074
## metab_58                      -0.0391098920
## metab_59                       0.2545021184
## metab_60                      -0.1238079824
## metab_61                       0.2045150013
## metab_62                      -0.0558297071
## metab_63                      -0.0578015302
## metab_64                       0.1372523796
## metab_65                       0.1068148068
## metab_66                      -0.0560738506
## metab_67                      -0.0885504372
## metab_68                       0.0559271234
## metab_69                       0.0323735953
## metab_70                       0.0737419387
## metab_71                      -0.3565062531
## metab_72                      -0.0204269619
## metab_73                      -0.1764151392
## metab_74                      -0.0375749523
## metab_75                       0.2934356894
## metab_76                      -0.1358354294
## metab_77                       0.0028609744
## metab_78                      -0.1822954707
## metab_79                       0.0128901575
## metab_80                       0.1367655608
## metab_81                       0.4514590233
## metab_82                      -0.4195053256
## metab_83                      -0.2226774898
## metab_84                      -0.1189751089
## metab_85                       0.0729523484
## metab_86                       0.0355370361
## metab_87                       0.1655933448
## metab_88                       0.2870479032
## metab_89                      -0.1363376335
## metab_90                      -0.1667274159
## metab_91                       0.0830913441
## metab_92                       0.1253420831
## metab_93                      -0.1735514917
## metab_94                      -0.0439978886
## metab_95                       0.7292625735
## metab_96                       0.2833287294
## metab_97                      -0.0083098327
## metab_98                      -0.0575887960
## metab_99                      -0.1386461788
## metab_100                      0.2378170209
## metab_101                      0.0426243034
## metab_102                      0.2191330260
## metab_103                      0.1866341219
## metab_104                      0.2763372587
## metab_105                      0.0984997675
## metab_106                      0.0328896314
## metab_107                      0.1613021683
## metab_108                      0.2529959282
## metab_109                     -0.0802225570
## metab_110                     -0.1381237953
## metab_111                     -0.2552546502
## metab_112                      0.0429241595
## metab_113                      0.4407947243
## metab_114                      0.2838332373
## metab_115                      0.3360216746
## metab_116                     -0.2440569379
## metab_117                     -0.2463183538
## metab_118                     -0.3776606445
## metab_119                     -0.1158462092
## metab_120                     -0.2979398104
## metab_121                     -0.1861150168
## metab_122                     -0.3385493562
## metab_123                     -0.2744617637
## metab_124                     -0.1482200696
## metab_125                     -0.0574693311
## metab_126                     -0.0504192509
## metab_127                     -0.1130907830
## metab_128                     -0.2014293379
## metab_129                      0.0436769002
## metab_130                     -0.4066108734
## metab_131                     -0.1014991614
## metab_132                      0.0115365688
## metab_133                     -0.4496445630
## metab_134                      0.1808691855
## metab_135                      0.0382172341
## metab_136                     -0.2553028557
## metab_137                      0.0481165040
## metab_138                     -0.0332786021
## metab_139                      0.1838214411
## metab_140                     -0.1436916780
## metab_141                     -0.1643696043
## metab_142                     -0.3210381940
## metab_143                     -0.2046510206
## metab_144                      0.2362733668
## metab_145                     -0.4474093473
## metab_146                     -0.2478010006
## metab_147                      0.1175383288
## metab_148                      0.1270776122
## metab_149                     -0.1266463449
## metab_150                      0.1120017283
## metab_151                      0.1174044898
## metab_152                     -0.0680622988
## metab_153                     -0.1549243474
## metab_154                      0.0059712815
## metab_155                     -0.1312489344
## metab_156                     -0.1514464586
## metab_157                      0.0879938991
## metab_158                      0.1395521566
## metab_159                      0.0991797155
## metab_160                     -0.5309867132
## metab_161                      1.2417573426
## metab_162                      0.0587041479
## metab_163                      0.6143989325
## metab_164                      0.1112577644
## metab_165                     -0.0184690014
## metab_166                     -0.2298261668
## metab_167                     -0.0117753978
## metab_168                     -0.1315176028
## metab_169                     -0.1046103335
## metab_170                     -0.1341008606
## metab_171                     -0.0106993433
## metab_172                     -0.2587978537
## metab_173                      0.4844551782
## metab_174                     -0.2304842382
## metab_175                      0.0602172097
## metab_176                      0.1891704474
## metab_177                      0.1613095211
ridge_predictions <- predict(ridge_model, s = best_lambda, newx = x_test, type = "response")

# convert probabilities to binary predictions
binary_predictions <- ifelse(ridge_predictions > 0.5, 1, 0)

# make sure levels match between binary_predictions and y_test
binary_predictions <- factor(binary_predictions, levels = c(0, 1))
y_test <- factor(y_test, levels = c(0, 1))

# accuracy accuracy
accuracy <- mean(binary_predictions == y_test)
cat("Ridge Accuracy on Test Set:", accuracy, "\n")
## Ridge Accuracy on Test Set: 0.7206704
conf_matrix <- confusionMatrix(binary_predictions, y_test)
conf_matrix
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 123  44
##          1  56 135
##                                           
##                Accuracy : 0.7207          
##                  95% CI : (0.6711, 0.7665)
##     No Information Rate : 0.5             
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.4413          
##                                           
##  Mcnemar's Test P-Value : 0.2713          
##                                           
##             Sensitivity : 0.6872          
##             Specificity : 0.7542          
##          Pos Pred Value : 0.7365          
##          Neg Pred Value : 0.7068          
##              Prevalence : 0.5000          
##          Detection Rate : 0.3436          
##    Detection Prevalence : 0.4665          
##       Balanced Accuracy : 0.7207          
##                                           
##        'Positive' Class : 0               
## 
# ROC Curve and AUC
roc_curve <- roc(as.numeric(y_test), as.numeric(ridge_predictions))
## Setting levels: control = 1, case = 2
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for Ridge Model")

auc_value <- auc(roc_curve)
cat("Ridge AUC on Test Set:", auc_value, "\n")
## Ridge AUC on Test Set: 0.8011922

Elastic

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[ trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who ~ . - hs_zbmi_who_binary, train_data)[,-1]
y_train <- train_data$hs_zbmi_who
x_test <- model.matrix(hs_zbmi_who ~ . - hs_zbmi_who_binary, test_data)[,-1]
y_test <- test_data$hs_zbmi_who

enet_model <- cv.glmnet(x_train, y_train, alpha = 0.5, family = "gaussian")
plot(enet_model)

enet_model$lambda.min
## [1] 0.01263519
coef(enet_model, s = enet_model$lambda.min)
## 240 x 1 sparse Matrix of class "dgCMatrix"
##                                         s1
## (Intercept)                    8.578351892
## hs_child_age_None             -0.115863248
## h_cohort2                     -0.199517040
## h_cohort3                      0.226486455
## h_cohort4                      0.270706077
## h_cohort5                      .          
## h_cohort6                      0.080649371
## e3_sex_Nonemale                0.331314265
## e3_yearbir_None2004           -0.103535525
## e3_yearbir_None2005           -0.039765996
## e3_yearbir_None2006            0.043243559
## e3_yearbir_None2007            0.068552528
## e3_yearbir_None2008            .          
## e3_yearbir_None2009            0.445442699
## h_edumc_None2                  .          
## h_edumc_None3                  0.054491500
## h_native_None1                 .          
## h_native_None2                 0.034320469
## hs_cd_c_Log2                   0.003067315
## hs_co_c_Log2                   .          
## hs_cs_c_Log2                   0.107718759
## hs_cu_c_Log2                   0.168073040
## hs_hg_c_Log2                  -0.047465586
## hs_mo_c_Log2                  -0.047744918
## hs_pb_c_Log2                   .          
## hs_dde_cadj_Log2              -0.020451748
## hs_pcb153_cadj_Log2           -0.219706322
## hs_pcb170_cadj_Log2           -0.035112266
## hs_dep_cadj_Log2              -0.011132999
## hs_pbde153_cadj_Log2          -0.016222997
## hs_pfhxs_c_Log2                .          
## hs_pfoa_c_Log2                -0.032627881
## hs_pfos_c_Log2                 0.008348682
## hs_prpa_cadj_Log2             -0.009537863
## hs_mbzp_cadj_Log2              0.053475790
## hs_mibp_cadj_Log2              .          
## hs_mnbp_cadj_Log2             -0.002706282
## h_bfdur_Ter(10.8,34.9]         0.101043321
## h_bfdur_Ter(34.9,Inf]          0.124373658
## hs_bakery_prod_Ter(2,6]        0.018983276
## hs_bakery_prod_Ter(6,Inf]     -0.087478595
## hs_dairy_Ter(14.6,25.6]       -0.007705120
## hs_dairy_Ter(25.6,Inf]         0.069664607
## hs_fastfood_Ter(0.132,0.5]     .          
## hs_fastfood_Ter(0.5,Inf]      -0.019016401
## hs_org_food_Ter(0.132,1]       0.039322506
## hs_org_food_Ter(1,Inf]         0.015758438
## hs_readymade_Ter(0.132,0.5]    0.078026127
## hs_readymade_Ter(0.5,Inf]      0.054721344
## hs_total_bread_Ter(7,17.5]     .          
## hs_total_bread_Ter(17.5,Inf]   .          
## hs_total_fish_Ter(1.5,3]       .          
## hs_total_fish_Ter(3,Inf]      -0.043448319
## hs_total_fruits_Ter(7,14.1]    0.080944909
## hs_total_fruits_Ter(14.1,Inf]  0.126550300
## hs_total_lipids_Ter(3,7]       0.060602634
## hs_total_lipids_Ter(7,Inf]     .          
## hs_total_potatoes_Ter(3,4]     0.009693939
## hs_total_potatoes_Ter(4,Inf]   .          
## hs_total_sweets_Ter(4.1,8.5]   .          
## hs_total_sweets_Ter(8.5,Inf]   .          
## hs_total_veg_Ter(6,8.5]        0.026747318
## hs_total_veg_Ter(8.5,Inf]     -0.006850275
## metab_1                       -0.020808800
## metab_2                        0.096683977
## metab_3                        0.031072809
## metab_4                        0.003171039
## metab_5                        0.445974148
## metab_6                       -0.105161707
## metab_7                        0.005410952
## metab_8                        0.234963593
## metab_9                        .          
## metab_10                       0.028167489
## metab_11                       0.179658243
## metab_12                      -0.146803264
## metab_13                       .          
## metab_14                      -0.443178624
## metab_15                       .          
## metab_16                       .          
## metab_17                      -0.006140514
## metab_18                      -0.171479325
## metab_19                       .          
## metab_20                       .          
## metab_21                       0.047522305
## metab_22                      -0.238392630
## metab_23                       0.136406835
## metab_24                       0.627204646
## metab_25                      -0.126974841
## metab_26                      -0.244950868
## metab_27                       0.493623258
## metab_28                       .          
## metab_29                      -0.022190986
## metab_30                       0.147834978
## metab_31                       0.051202465
## metab_32                      -0.136067374
## metab_33                       .          
## metab_34                       .          
## metab_35                       .          
## metab_36                       .          
## metab_37                      -0.042637486
## metab_38                      -0.060170781
## metab_39                       .          
## metab_40                       0.069886895
## metab_41                       0.249082893
## metab_42                      -0.414203858
## metab_43                      -0.164870171
## metab_44                      -0.052613203
## metab_45                       0.126989129
## metab_46                       .          
## metab_47                       0.451687523
## metab_48                      -0.769383671
## metab_49                       0.121626575
## metab_50                      -0.195490856
## metab_51                       .          
## metab_52                       0.437724646
## metab_53                       .          
## metab_54                       0.117392944
## metab_55                       .          
## metab_56                      -0.128140519
## metab_57                       .          
## metab_58                       .          
## metab_59                       0.585488747
## metab_60                      -0.145473912
## metab_61                       .          
## metab_62                       .          
## metab_63                      -0.155176645
## metab_64                       .          
## metab_65                       .          
## metab_66                      -0.079016208
## metab_67                      -0.231657476
## metab_68                       0.115684723
## metab_69                      -0.053817763
## metab_70                       .          
## metab_71                      -0.075636786
## metab_72                       .          
## metab_73                      -0.113840395
## metab_74                       .          
## metab_75                       0.291789027
## metab_76                       .          
## metab_77                       0.012878526
## metab_78                      -0.144180621
## metab_79                       .          
## metab_80                       .          
## metab_81                       .          
## metab_82                      -0.663922686
## metab_83                       .          
## metab_84                      -0.094860108
## metab_85                       .          
## metab_86                       0.357294893
## metab_87                       0.064179237
## metab_88                       0.574755853
## metab_89                      -1.143000128
## metab_90                       .          
## metab_91                       0.135199218
## metab_92                       0.109637762
## metab_93                       .          
## metab_94                      -0.059295586
## metab_95                       1.499983404
## metab_96                       0.051363171
## metab_97                       .          
## metab_98                       .          
## metab_99                      -0.433436320
## metab_100                      0.577311913
## metab_101                      .          
## metab_102                      .          
## metab_103                     -0.435522691
## metab_104                      0.175872915
## metab_105                      0.140581911
## metab_106                      0.088994443
## metab_107                      0.047991077
## metab_108                      .          
## metab_109                     -0.258584717
## metab_110                     -0.169475959
## metab_111                      .          
## metab_112                      .          
## metab_113                      0.640532268
## metab_114                      .          
## metab_115                      0.528199313
## metab_116                      .          
## metab_117                      .          
## metab_118                     -0.339965015
## metab_119                      .          
## metab_120                     -0.274743544
## metab_121                      .          
## metab_122                     -0.073184707
## metab_123                      .          
## metab_124                      .          
## metab_125                     -0.179193784
## metab_126                      .          
## metab_127                     -0.024652725
## metab_128                     -0.005445981
## metab_129                      .          
## metab_130                      .          
## metab_131                      .          
## metab_132                      .          
## metab_133                     -0.320335848
## metab_134                      0.327507471
## metab_135                     -0.226372203
## metab_136                      .          
## metab_137                     -0.393600744
## metab_138                     -0.519594951
## metab_139                      .          
## metab_140                     -0.016402886
## metab_141                      .          
## metab_142                     -0.577761021
## metab_143                     -0.268800773
## metab_144                      0.005096758
## metab_145                     -0.200534322
## metab_146                     -0.001492012
## metab_147                      0.516271413
## metab_148                      .          
## metab_149                      .          
## metab_150                      0.273289288
## metab_151                     -0.001296237
## metab_152                     -0.045905617
## metab_153                      .          
## metab_154                     -0.018929928
## metab_155                     -0.333286274
## metab_156                      .          
## metab_157                      0.180931535
## metab_158                      .          
## metab_159                      0.137589540
## metab_160                     -2.001321991
## metab_161                      2.313776131
## metab_162                      .          
## metab_163                      0.629853044
## metab_164                     -0.090531303
## metab_165                      .          
## metab_166                     -0.380179693
## metab_167                     -0.088266549
## metab_168                     -0.012943947
## metab_169                      .          
## metab_170                      .          
## metab_171                     -0.076154014
## metab_172                      .          
## metab_173                      0.061244506
## metab_174                      .          
## metab_175                     -0.217032699
## metab_176                     -0.049665193
## metab_177                      0.132238749
predictions <- predict(enet_model, s = enet_model$lambda.min, newx = x_test)

test_mse <- mean((predictions - y_test)^2)
cat("Mean Squared Error on Test Set:", test_mse, "\n")
## Mean Squared Error on Test Set: 0.7364518
# convert hs_zbmi_who to binary based on median
median_value <- median(selected_metabolomics_data$hs_zbmi_who, na.rm = TRUE)
selected_metabolomics_data$hs_zbmi_who_binary <- ifelse(selected_metabolomics_data$hs_zbmi_who > median_value, 1, 0)

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who_binary, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, train_data)[,-1]
y_train <- train_data$hs_zbmi_who_binary
x_test <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, test_data)[,-1]
y_test <- test_data$hs_zbmi_who_binary

# fit enet model using cross-validation
enet_model <- cv.glmnet(x_train, y_train, alpha = 0.5, family = "binomial")
plot(enet_model)

best_lambda <- enet_model$lambda.min
cat("Best Lambda:", best_lambda, "\n")
## Best Lambda: 0.01922375
coef(enet_model, s = best_lambda)
## 240 x 1 sparse Matrix of class "dgCMatrix"
##                                          s1
## (Intercept)                    2.4020477436
## hs_child_age_None             -0.0560014051
## h_cohort2                     -0.4073651020
## h_cohort3                      .           
## h_cohort4                      .           
## h_cohort5                      .           
## h_cohort6                      .           
## e3_sex_Nonemale                0.1634352085
## e3_yearbir_None2004           -0.3111975187
## e3_yearbir_None2005           -0.0274407810
## e3_yearbir_None2006            0.0547947452
## e3_yearbir_None2007            .           
## e3_yearbir_None2008            .           
## e3_yearbir_None2009            0.8681768833
## h_edumc_None2                  0.0650518497
## h_edumc_None3                  .           
## h_native_None1                 .           
## h_native_None2                 0.4274276556
## hs_cd_c_Log2                   .           
## hs_co_c_Log2                   .           
## hs_cs_c_Log2                   0.0326280011
## hs_cu_c_Log2                   .           
## hs_hg_c_Log2                   .           
## hs_mo_c_Log2                  -0.0342030845
## hs_pb_c_Log2                   .           
## hs_dde_cadj_Log2              -0.0034750012
## hs_pcb153_cadj_Log2           -0.2942329613
## hs_pcb170_cadj_Log2           -0.0222308611
## hs_dep_cadj_Log2              -0.0209386238
## hs_pbde153_cadj_Log2          -0.0449801939
## hs_pfhxs_c_Log2                .           
## hs_pfoa_c_Log2                -0.2664887408
## hs_pfos_c_Log2                 .           
## hs_prpa_cadj_Log2              .           
## hs_mbzp_cadj_Log2              0.0066356831
## hs_mibp_cadj_Log2              .           
## hs_mnbp_cadj_Log2             -0.0023050433
## h_bfdur_Ter(10.8,34.9]         0.0988547127
## h_bfdur_Ter(34.9,Inf]          0.0147006452
## hs_bakery_prod_Ter(2,6]        .           
## hs_bakery_prod_Ter(6,Inf]     -0.2924949144
## hs_dairy_Ter(14.6,25.6]        .           
## hs_dairy_Ter(25.6,Inf]         .           
## hs_fastfood_Ter(0.132,0.5]     .           
## hs_fastfood_Ter(0.5,Inf]       .           
## hs_org_food_Ter(0.132,1]       0.0487143467
## hs_org_food_Ter(1,Inf]         0.0774958323
## hs_readymade_Ter(0.132,0.5]    .           
## hs_readymade_Ter(0.5,Inf]      .           
## hs_total_bread_Ter(7,17.5]    -0.0209828411
## hs_total_bread_Ter(17.5,Inf]   .           
## hs_total_fish_Ter(1.5,3]       .           
## hs_total_fish_Ter(3,Inf]       .           
## hs_total_fruits_Ter(7,14.1]    .           
## hs_total_fruits_Ter(14.1,Inf]  0.0394897294
## hs_total_lipids_Ter(3,7]       .           
## hs_total_lipids_Ter(7,Inf]     .           
## hs_total_potatoes_Ter(3,4]     0.0034319177
## hs_total_potatoes_Ter(4,Inf]  -0.0753743752
## hs_total_sweets_Ter(4.1,8.5]   .           
## hs_total_sweets_Ter(8.5,Inf]   .           
## hs_total_veg_Ter(6,8.5]        0.1062968323
## hs_total_veg_Ter(8.5,Inf]     -0.1091028878
## metab_1                        .           
## metab_2                        .           
## metab_3                        .           
## metab_4                        0.1031376233
## metab_5                        0.7634800567
## metab_6                        .           
## metab_7                        .           
## metab_8                        0.2601092101
## metab_9                       -0.0068450365
## metab_10                       .           
## metab_11                       .           
## metab_12                      -0.0269087755
## metab_13                       .           
## metab_14                       .           
## metab_15                       .           
## metab_16                       .           
## metab_17                       .           
## metab_18                       .           
## metab_19                       .           
## metab_20                       .           
## metab_21                       .           
## metab_22                      -0.0013508870
## metab_23                       0.0904894843
## metab_24                       0.2189482566
## metab_25                       .           
## metab_26                      -0.4024123986
## metab_27                       .           
## metab_28                       0.3841973716
## metab_29                       .           
## metab_30                       0.0732898024
## metab_31                       .           
## metab_32                       .           
## metab_33                       .           
## metab_34                       .           
## metab_35                       .           
## metab_36                       0.4249850652
## metab_37                      -0.1096358525
## metab_38                      -0.3348966019
## metab_39                       .           
## metab_40                       .           
## metab_41                       .           
## metab_42                       .           
## metab_43                       .           
## metab_44                       .           
## metab_45                       .           
## metab_46                      -0.0922234432
## metab_47                       0.4151670014
## metab_48                      -0.8444050484
## metab_49                       0.7696982049
## metab_50                      -0.2442075003
## metab_51                       .           
## metab_52                       .           
## metab_53                       .           
## metab_54                       0.0629050382
## metab_55                       .           
## metab_56                       .           
## metab_57                       .           
## metab_58                       .           
## metab_59                       0.2754506887
## metab_60                       .           
## metab_61                       .           
## metab_62                       .           
## metab_63                       .           
## metab_64                       .           
## metab_65                       0.0471572094
## metab_66                       .           
## metab_67                       .           
## metab_68                       .           
## metab_69                       .           
## metab_70                       .           
## metab_71                      -0.3145978213
## metab_72                       .           
## metab_73                       .           
## metab_74                       .           
## metab_75                       .           
## metab_76                       .           
## metab_77                       .           
## metab_78                       .           
## metab_79                       .           
## metab_80                       .           
## metab_81                       0.6542405688
## metab_82                      -0.8624167458
## metab_83                       .           
## metab_84                       .           
## metab_85                       .           
## metab_86                       .           
## metab_87                       .           
## metab_88                       .           
## metab_89                       .           
## metab_90                       .           
## metab_91                       .           
## metab_92                       0.0477387700
## metab_93                       .           
## metab_94                       .           
## metab_95                       1.6775299871
## metab_96                       .           
## metab_97                       .           
## metab_98                       .           
## metab_99                       .           
## metab_100                      .           
## metab_101                      .           
## metab_102                      .           
## metab_103                      .           
## metab_104                      0.3021326705
## metab_105                      .           
## metab_106                      .           
## metab_107                      .           
## metab_108                      .           
## metab_109                      .           
## metab_110                      .           
## metab_111                     -0.0217730053
## metab_112                      .           
## metab_113                      0.5047685046
## metab_114                      .           
## metab_115                      0.2196103381
## metab_116                     -0.2148789307
## metab_117                      .           
## metab_118                     -0.6877284976
## metab_119                      .           
## metab_120                     -0.1959035770
## metab_121                      .           
## metab_122                     -0.6430105205
## metab_123                     -0.3036600651
## metab_124                      .           
## metab_125                      .           
## metab_126                      .           
## metab_127                     -0.1296679747
## metab_128                     -0.0223137651
## metab_129                      .           
## metab_130                     -0.0709113161
## metab_131                      .           
## metab_132                      .           
## metab_133                     -0.5420970043
## metab_134                      .           
## metab_135                      .           
## metab_136                      .           
## metab_137                      .           
## metab_138                      .           
## metab_139                      .           
## metab_140                      .           
## metab_141                      .           
## metab_142                     -0.1885139404
## metab_143                      .           
## metab_144                      .           
## metab_145                     -0.5316793004
## metab_146                     -0.1148885375
## metab_147                      .           
## metab_148                      .           
## metab_149                      .           
## metab_150                      0.0160259618
## metab_151                      0.0807523014
## metab_152                     -0.0698930172
## metab_153                      .           
## metab_154                      .           
## metab_155                      .           
## metab_156                      .           
## metab_157                      .           
## metab_158                      .           
## metab_159                      .           
## metab_160                     -1.7695413881
## metab_161                      2.7371423123
## metab_162                      .           
## metab_163                      0.3055854670
## metab_164                      .           
## metab_165                      .           
## metab_166                     -0.0421310230
## metab_167                      .           
## metab_168                     -0.0009165542
## metab_169                      .           
## metab_170                     -0.1220026556
## metab_171                      .           
## metab_172                     -0.3375446638
## metab_173                      0.6102159262
## metab_174                      .           
## metab_175                      .           
## metab_176                      .           
## metab_177                      0.1029920014
enet_predictions <- predict(enet_model, s = best_lambda, newx = x_test, type = "response")

# convert probabilities to binary predictions
binary_predictions <- ifelse(enet_predictions > 0.5, 1, 0)

# make sure levels match between binary_predictions and y_test
binary_predictions <- factor(binary_predictions, levels = c(0, 1))
y_test <- factor(y_test, levels = c(0, 1))

# accuracy accuracy
accuracy <- mean(binary_predictions == y_test)
cat("Ridge Accuracy on Test Set:", accuracy, "\n")
## Ridge Accuracy on Test Set: 0.7318436
conf_matrix <- confusionMatrix(binary_predictions, y_test)
conf_matrix
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 131  48
##          1  48 131
##                                          
##                Accuracy : 0.7318         
##                  95% CI : (0.6828, 0.777)
##     No Information Rate : 0.5            
##     P-Value [Acc > NIR] : <2e-16         
##                                          
##                   Kappa : 0.4637         
##                                          
##  Mcnemar's Test P-Value : 1              
##                                          
##             Sensitivity : 0.7318         
##             Specificity : 0.7318         
##          Pos Pred Value : 0.7318         
##          Neg Pred Value : 0.7318         
##              Prevalence : 0.5000         
##          Detection Rate : 0.3659         
##    Detection Prevalence : 0.5000         
##       Balanced Accuracy : 0.7318         
##                                          
##        'Positive' Class : 0              
## 
# ROC Curve and AUC
roc_curve <- roc(as.numeric(y_test), as.numeric(enet_predictions))
## Setting levels: control = 1, case = 2
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for Elastic Net Model")

auc_value <- auc(roc_curve)
cat("Elastic Net AUC on Test Set:", auc_value, "\n")
## Elastic Net AUC on Test Set: 0.8029088

Random Forest

set.seed(101)
rf_model <- randomForest(hs_zbmi_who ~ . -hs_zbmi_who_binary, data = train_data, ntree = 500)

rf_predictions <- predict(rf_model, newdata = test_data)

rf_mse <- mean((rf_predictions - y_test)^2)
cat("Random Forest Mean Squared Error on Test Set:", rf_mse, "\n")
## Random Forest Mean Squared Error on Test Set: NA
importance(rf_model)
##                       IncNodePurity
## hs_child_age_None         5.5074522
## h_cohort                 19.4916857
## e3_sex_None               0.4492505
## e3_yearbir_None           5.8039370
## h_edumc_None              1.4385402
## h_native_None             1.7658986
## hs_cd_c_Log2              5.6183507
## hs_co_c_Log2              4.4794448
## hs_cs_c_Log2              4.8703163
## hs_cu_c_Log2              8.5678120
## hs_hg_c_Log2              6.4784728
## hs_mo_c_Log2              6.7818712
## hs_pb_c_Log2              4.6451124
## hs_dde_cadj_Log2         19.5653594
## hs_pcb153_cadj_Log2      17.0696101
## hs_pcb170_cadj_Log2      52.7773388
## hs_dep_cadj_Log2          6.7184329
## hs_pbde153_cadj_Log2     16.8722302
## hs_pfhxs_c_Log2           6.6002292
## hs_pfoa_c_Log2           13.1283651
## hs_pfos_c_Log2            8.8809389
## hs_prpa_cadj_Log2         5.6488812
## hs_mbzp_cadj_Log2         4.7983076
## hs_mibp_cadj_Log2         4.2370823
## hs_mnbp_cadj_Log2         4.9558276
## h_bfdur_Ter               1.2575134
## hs_bakery_prod_Ter        2.9254318
## hs_dairy_Ter              1.2260774
## hs_fastfood_Ter           0.9047281
## hs_org_food_Ter           1.5336253
## hs_readymade_Ter          1.3668650
## hs_total_bread_Ter        1.0428489
## hs_total_fish_Ter         1.3550813
## hs_total_fruits_Ter       1.0898909
## hs_total_lipids_Ter       1.0470290
## hs_total_potatoes_Ter     0.9123339
## hs_total_sweets_Ter       1.6372221
## hs_total_veg_Ter          1.4580138
## metab_1                   4.0871578
## metab_2                   4.2128177
## metab_3                   4.7029776
## metab_4                   5.8636216
## metab_5                   4.5489668
## metab_6                   9.8393989
## metab_7                   4.3061556
## metab_8                  36.1438350
## metab_9                   3.1976746
## metab_10                  3.6374170
## metab_11                  3.7559461
## metab_12                  2.4729509
## metab_13                  3.0108598
## metab_14                  3.8064562
## metab_15                  3.2799798
## metab_16                  2.2249745
## metab_17                  2.9852186
## metab_18                  1.9925296
## metab_19                  2.7307790
## metab_20                  3.7053660
## metab_21                  2.1785723
## metab_22                  1.9225963
## metab_23                  2.0059957
## metab_24                  2.3489537
## metab_25                  3.9994896
## metab_26                  6.8505449
## metab_27                  2.5988484
## metab_28                  3.8400569
## metab_29                  3.1568753
## metab_30                 19.8615408
## metab_31                  3.9556422
## metab_32                  2.8956486
## metab_33                  5.0415088
## metab_34                  1.9760372
## metab_35                  6.6564642
## metab_36                  3.1010204
## metab_37                  2.6569784
## metab_38                  2.4040112
## metab_39                  2.4260736
## metab_40                  3.8362923
## metab_41                  3.6742931
## metab_42                  2.3948847
## metab_43                  3.0761983
## metab_44                  2.8462257
## metab_45                  3.4434926
## metab_46                  4.9750622
## metab_47                  7.6679729
## metab_48                 11.7097595
## metab_49                 53.5181385
## metab_50                  9.2778981
## metab_51                  4.7769057
## metab_52                  5.9956658
## metab_53                  5.0377482
## metab_54                  5.7990430
## metab_55                  4.5033979
## metab_56                  4.2665208
## metab_57                  4.5263447
## metab_58                  2.8768517
## metab_59                  6.8572432
## metab_60                  4.5240185
## metab_61                  3.0325074
## metab_62                  3.7119392
## metab_63                  3.4153570
## metab_64                  4.1487240
## metab_65                  3.1945214
## metab_66                  2.8112278
## metab_67                  3.2072152
## metab_68                  3.9196796
## metab_69                  2.7667018
## metab_70                  3.6862662
## metab_71                  3.5275714
## metab_72                  3.1849869
## metab_73                  3.2050063
## metab_74                  2.6949838
## metab_75                  3.6272659
## metab_76                  2.9534465
## metab_77                  4.7055225
## metab_78                  5.4798728
## metab_79                  3.8960521
## metab_80                  3.6397873
## metab_81                  3.0255419
## metab_82                  4.2731811
## metab_83                  3.1672685
## metab_84                  3.3761037
## metab_85                  7.1480799
## metab_86                  3.0342445
## metab_87                  3.1990462
## metab_88                  3.1502847
## metab_89                  2.0640603
## metab_90                  3.1518544
## metab_91                  3.8310605
## metab_92                  2.9746674
## metab_93                  2.6820865
## metab_94                  9.3598587
## metab_95                 52.5632971
## metab_96                 13.1494768
## metab_97                  3.0896610
## metab_98                  3.7069636
## metab_99                  5.7433224
## metab_100                 3.1887943
## metab_101                 3.1908409
## metab_102                 5.2689107
## metab_103                 2.5897429
## metab_104                 4.2242263
## metab_105                 3.8655538
## metab_106                 3.0282458
## metab_107                 3.3185893
## metab_108                 3.4897988
## metab_109                 4.4365747
## metab_110                 4.9830908
## metab_111                 3.1476995
## metab_112                 2.8362703
## metab_113                 4.4385828
## metab_114                 3.4837432
## metab_115                 4.7996199
## metab_116                 6.6046162
## metab_117                 5.1747420
## metab_118                 3.3627455
## metab_119                 5.8751976
## metab_120                 7.6859256
## metab_121                 4.4947484
## metab_122                 6.7219227
## metab_123                 3.5101852
## metab_124                 4.0121806
## metab_125                 2.9179718
## metab_126                 2.5829507
## metab_127                 5.0579414
## metab_128                 8.5064765
## metab_129                 3.4979494
## metab_130                 4.0003071
## metab_131                 2.5970924
## metab_132                 2.7297049
## metab_133                 2.7821347
## metab_134                 3.8032324
## metab_135                 4.8982450
## metab_136                 5.3801748
## metab_137                 5.1391792
## metab_138                 5.2830234
## metab_139                 3.8560108
## metab_140                 2.7863988
## metab_141                10.6921849
## metab_142                10.6114033
## metab_143                11.6015673
## metab_144                 3.0581726
## metab_145                 5.4116243
## metab_146                 6.6799793
## metab_147                 4.3133137
## metab_148                 3.9434950
## metab_149                 4.4806132
## metab_150                 4.3264355
## metab_151                 3.4339273
## metab_152                 5.9309425
## metab_153                 6.7072909
## metab_154                 6.2609053
## metab_155                 2.5536669
## metab_156                 2.5273062
## metab_157                 3.3192833
## metab_158                 2.6606954
## metab_159                 2.8835429
## metab_160                 7.2901430
## metab_161                16.0767528
## metab_162                 3.5712194
## metab_163                 8.9745145
## metab_164                 7.0366866
## metab_165                 3.5349826
## metab_166                 2.8503588
## metab_167                 3.1266057
## metab_168                 3.2890921
## metab_169                 3.9190006
## metab_170                 4.7075326
## metab_171                 6.9721360
## metab_172                 4.6671661
## metab_173                 5.1196117
## metab_174                 3.4247350
## metab_175                 4.9665905
## metab_176                 6.1612095
## metab_177                 8.3370310
varImpPlot(rf_model)

# ROC Curve and AUC
roc_curve <- roc(as.numeric(as.character(y_test)), as.numeric(as.character(rf_predictions)))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for Random Forest Model")

auc_value <- auc(roc_curve)
cat("Random Forest AUC on Test Set:", auc_value, "\n")
## Random Forest AUC on Test Set: 0.7725726
selected_metabolomics_data <- selected_metabolomics_data %>% na.omit()

# hs_zbmi_who to binary based on median
median_value <- median(selected_metabolomics_data$hs_zbmi_who, na.rm = TRUE)
selected_metabolomics_data$hs_zbmi_who_binary <- ifelse(selected_metabolomics_data$hs_zbmi_who > median_value, 1, 0)
selected_metabolomics_data$hs_zbmi_who_binary <- factor(selected_metabolomics_data$hs_zbmi_who_binary, levels = c(0, 1), labels = c("0", "1"))

set.seed(101)
trainIndex <- createDataPartition(selected_metabolomics_data$hs_zbmi_who_binary, p = .7, 
                                  list = FALSE, 
                                  times = 1)
train_data <- selected_metabolomics_data[trainIndex,]
test_data  <- selected_metabolomics_data[-trainIndex,]

x_train <- model.matrix(hs_zbmi_who_binary ~ . , train_data)[,-1]
y_train <- train_data$hs_zbmi_who_binary
x_test <- model.matrix(hs_zbmi_who_binary ~ . , test_data)[,-1]
y_test <- test_data$hs_zbmi_who_binary

set.seed(101)
rf_model <- randomForest(hs_zbmi_who_binary ~ . -hs_zbmi_who, data = train_data, ntree = 500)

rf_predictions_prob <- predict(rf_model, newdata = test_data, type = "prob")[,2]
rf_predictions <- predict(rf_model, newdata = test_data)

rf_mse <- mean((as.numeric(as.character(rf_predictions)) - as.numeric(as.character(y_test)))^2)
cat("Random Forest Mean Squared Error on Test Set:", rf_mse, "\n")
## Random Forest Mean Squared Error on Test Set: 0.3072626
importance(rf_model)
##                       MeanDecreaseGini
## hs_child_age_None            1.8523293
## h_cohort                     3.3479617
## e3_sex_None                  0.1040747
## e3_yearbir_None              1.3693376
## h_edumc_None                 0.4007728
## h_native_None                0.5716096
## hs_cd_c_Log2                 2.0735471
## hs_co_c_Log2                 1.6621328
## hs_cs_c_Log2                 2.1745413
## hs_cu_c_Log2                 2.1906329
## hs_hg_c_Log2                 2.0161000
## hs_mo_c_Log2                 2.1869577
## hs_pb_c_Log2                 1.9878770
## hs_dde_cadj_Log2             3.9288392
## hs_pcb153_cadj_Log2          5.3039284
## hs_pcb170_cadj_Log2          8.7092125
## hs_dep_cadj_Log2             2.4571462
## hs_pbde153_cadj_Log2         4.7637945
## hs_pfhxs_c_Log2              2.5413269
## hs_pfoa_c_Log2               4.1792489
## hs_pfos_c_Log2               3.0811819
## hs_prpa_cadj_Log2            2.0536045
## hs_mbzp_cadj_Log2            1.8033959
## hs_mibp_cadj_Log2            1.7484547
## hs_mnbp_cadj_Log2            1.7348190
## h_bfdur_Ter                  0.6339703
## hs_bakery_prod_Ter           0.5878442
## hs_dairy_Ter                 0.2434327
## hs_fastfood_Ter              0.1845531
## hs_org_food_Ter              0.2072968
## hs_readymade_Ter             0.3005943
## hs_total_bread_Ter           0.3357945
## hs_total_fish_Ter            0.4122144
## hs_total_fruits_Ter          0.2736450
## hs_total_lipids_Ter          0.3954569
## hs_total_potatoes_Ter        0.3891347
## hs_total_sweets_Ter          0.1939762
## hs_total_veg_Ter             0.5094748
## metab_1                      1.7109996
## metab_2                      2.1424708
## metab_3                      2.1151758
## metab_4                      3.5424401
## metab_5                      2.1797806
## metab_6                      2.2480108
## metab_7                      2.2489912
## metab_8                      4.2774417
## metab_9                      1.7610228
## metab_10                     1.7685733
## metab_11                     1.4575901
## metab_12                     1.6536111
## metab_13                     1.4001754
## metab_14                     1.6016016
## metab_15                     1.2990389
## metab_16                     1.7940074
## metab_17                     1.0069289
## metab_18                     1.3688455
## metab_19                     1.3142545
## metab_20                     1.6738605
## metab_21                     1.3146701
## metab_22                     1.1629587
## metab_23                     1.2397936
## metab_24                     1.5184173
## metab_25                     1.3403026
## metab_26                     1.8571963
## metab_27                     1.6379500
## metab_28                     2.7852755
## metab_29                     1.7570262
## metab_30                     3.5977656
## metab_31                     1.7964019
## metab_32                     1.4625578
## metab_33                     1.6468947
## metab_34                     1.0247106
## metab_35                     1.8056123
## metab_36                     1.7166192
## metab_37                     1.1014846
## metab_38                     1.1496938
## metab_39                     1.1905605
## metab_40                     1.3512653
## metab_41                     1.5383893
## metab_42                     1.1824578
## metab_43                     1.6879711
## metab_44                     1.5111428
## metab_45                     1.8191252
## metab_46                     1.6115893
## metab_47                     2.9455712
## metab_48                     2.7233195
## metab_49                     9.0757620
## metab_50                     2.1644236
## metab_51                     2.1874906
## metab_52                     1.9432381
## metab_53                     2.9044352
## metab_54                     2.9120093
## metab_55                     2.3686913
## metab_56                     2.2252842
## metab_57                     1.7873563
## metab_58                     1.4269410
## metab_59                     2.6388253
## metab_60                     1.7717135
## metab_61                     1.7858749
## metab_62                     1.7418597
## metab_63                     1.7856215
## metab_64                     1.5896259
## metab_65                     2.0104752
## metab_66                     1.5850147
## metab_67                     1.7720968
## metab_68                     1.6081484
## metab_69                     1.4655227
## metab_70                     1.6966824
## metab_71                     1.8969630
## metab_72                     1.8656166
## metab_73                     1.8975098
## metab_74                     1.3328979
## metab_75                     1.7640205
## metab_76                     2.0179031
## metab_77                     1.6029826
## metab_78                     2.2538563
## metab_79                     1.9218813
## metab_80                     2.0646595
## metab_81                     1.6624515
## metab_82                     2.1874769
## metab_83                     1.7090610
## metab_84                     1.6666232
## metab_85                     2.0956107
## metab_86                     1.6292567
## metab_87                     1.7897006
## metab_88                     1.4322982
## metab_89                     1.4487496
## metab_90                     1.7324393
## metab_91                     1.6481035
## metab_92                     1.7081247
## metab_93                     1.3216934
## metab_94                     2.4265592
## metab_95                     7.3691396
## metab_96                     4.6046467
## metab_97                     1.5680555
## metab_98                     1.7334903
## metab_99                     1.9842036
## metab_100                    1.4593013
## metab_101                    1.4962482
## metab_102                    2.9286482
## metab_103                    1.7995811
## metab_104                    2.0042121
## metab_105                    1.5233338
## metab_106                    1.7532421
## metab_107                    1.7044256
## metab_108                    1.5355808
## metab_109                    1.8251939
## metab_110                    2.3320165
## metab_111                    2.0128538
## metab_112                    1.7377734
## metab_113                    2.3712733
## metab_114                    1.6990983
## metab_115                    1.4007781
## metab_116                    2.6324561
## metab_117                    2.0493509
## metab_118                    1.9590967
## metab_119                    1.6945789
## metab_120                    2.1263983
## metab_121                    1.5200319
## metab_122                    2.7128775
## metab_123                    1.9272855
## metab_124                    1.8747739
## metab_125                    1.4552243
## metab_126                    1.7179112
## metab_127                    2.4613674
## metab_128                    1.6515006
## metab_129                    1.5716569
## metab_130                    1.8222297
## metab_131                    1.3981787
## metab_132                    1.2985384
## metab_133                    1.9020675
## metab_134                    1.7976656
## metab_135                    1.4393536
## metab_136                    1.5948977
## metab_137                    1.5721024
## metab_138                    1.8372330
## metab_139                    1.3633590
## metab_140                    1.2936696
## metab_141                    2.3115194
## metab_142                    2.2707234
## metab_143                    1.6900013
## metab_144                    1.5823535
## metab_145                    2.2555999
## metab_146                    2.2061952
## metab_147                    1.4162967
## metab_148                    1.6483307
## metab_149                    2.2464976
## metab_150                    1.7813079
## metab_151                    2.0734559
## metab_152                    1.9623828
## metab_153                    1.7961992
## metab_154                    2.2859253
## metab_155                    1.6463759
## metab_156                    1.5660346
## metab_157                    1.9665845
## metab_158                    1.3425696
## metab_159                    1.7602764
## metab_160                    1.8770333
## metab_161                    5.1306727
## metab_162                    2.0290646
## metab_163                    3.6280902
## metab_164                    2.5887911
## metab_165                    2.0201035
## metab_166                    1.5318234
## metab_167                    1.8498371
## metab_168                    1.8635521
## metab_169                    1.8239681
## metab_170                    1.9615842
## metab_171                    2.5313165
## metab_172                    1.8581499
## metab_173                    1.7592050
## metab_174                    1.8164449
## metab_175                    2.1994183
## metab_176                    3.2170862
## metab_177                    4.0289999
varImpPlot(rf_model)

# ROC Curve and AUC
roc_curve <- roc(as.numeric(as.character(y_test)), as.numeric(as.character(rf_predictions_prob)))
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for Random Forest Model")

auc_value <- auc(roc_curve)
cat("Random Forest AUC on Test Set:", auc_value, "\n")
## Random Forest AUC on Test Set: 0.7508193
conf_matrix <- confusionMatrix(rf_predictions, y_test)
print(conf_matrix)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 118  49
##          1  61 130
##                                           
##                Accuracy : 0.6927          
##                  95% CI : (0.6421, 0.7402)
##     No Information Rate : 0.5             
##     P-Value [Acc > NIR] : 1.131e-13       
##                                           
##                   Kappa : 0.3855          
##                                           
##  Mcnemar's Test P-Value : 0.2943          
##                                           
##             Sensitivity : 0.6592          
##             Specificity : 0.7263          
##          Pos Pred Value : 0.7066          
##          Neg Pred Value : 0.6806          
##              Prevalence : 0.5000          
##          Detection Rate : 0.3296          
##    Detection Prevalence : 0.4665          
##       Balanced Accuracy : 0.6927          
##                                           
##        'Positive' Class : 0               
##

GBM

set.seed(101)
gbm_model <- gbm(hs_zbmi_who ~ . - hs_zbmi_who_binary, data = train_data, 
                 distribution = "gaussian",
                 n.trees = 1000,
                 interaction.depth = 3,
                 n.minobsinnode = 10,
                 shrinkage = 0.01,
                 cv.folds = 5,
                 verbose = TRUE)
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        1.4345             nan     0.0100    0.0030
##      2        1.4303             nan     0.0100    0.0026
##      3        1.4256             nan     0.0100    0.0034
##      4        1.4212             nan     0.0100    0.0030
##      5        1.4167             nan     0.0100    0.0023
##      6        1.4125             nan     0.0100    0.0025
##      7        1.4080             nan     0.0100    0.0036
##      8        1.4038             nan     0.0100    0.0028
##      9        1.3986             nan     0.0100    0.0040
##     10        1.3936             nan     0.0100    0.0030
##     20        1.3502             nan     0.0100    0.0038
##     40        1.2714             nan     0.0100    0.0025
##     60        1.2058             nan     0.0100    0.0014
##     80        1.1486             nan     0.0100    0.0021
##    100        1.0992             nan     0.0100    0.0010
##    120        1.0544             nan     0.0100    0.0005
##    140        1.0151             nan     0.0100    0.0006
##    160        0.9758             nan     0.0100    0.0008
##    180        0.9415             nan     0.0100    0.0004
##    200        0.9107             nan     0.0100    0.0004
##    220        0.8806             nan     0.0100    0.0001
##    240        0.8517             nan     0.0100    0.0010
##    260        0.8253             nan     0.0100    0.0000
##    280        0.8012             nan     0.0100    0.0007
##    300        0.7783             nan     0.0100   -0.0001
##    320        0.7566             nan     0.0100    0.0004
##    340        0.7376             nan     0.0100    0.0001
##    360        0.7170             nan     0.0100    0.0002
##    380        0.6984             nan     0.0100   -0.0005
##    400        0.6823             nan     0.0100    0.0005
##    420        0.6650             nan     0.0100    0.0000
##    440        0.6492             nan     0.0100    0.0001
##    460        0.6339             nan     0.0100    0.0003
##    480        0.6201             nan     0.0100    0.0000
##    500        0.6070             nan     0.0100   -0.0001
##    520        0.5947             nan     0.0100    0.0003
##    540        0.5821             nan     0.0100   -0.0002
##    560        0.5698             nan     0.0100    0.0002
##    580        0.5582             nan     0.0100    0.0001
##    600        0.5472             nan     0.0100   -0.0000
##    620        0.5361             nan     0.0100    0.0000
##    640        0.5259             nan     0.0100   -0.0001
##    660        0.5166             nan     0.0100   -0.0001
##    680        0.5066             nan     0.0100    0.0001
##    700        0.4975             nan     0.0100   -0.0002
##    720        0.4888             nan     0.0100    0.0003
##    740        0.4798             nan     0.0100   -0.0000
##    760        0.4710             nan     0.0100   -0.0000
##    780        0.4626             nan     0.0100   -0.0002
##    800        0.4546             nan     0.0100   -0.0001
##    820        0.4469             nan     0.0100   -0.0002
##    840        0.4394             nan     0.0100   -0.0001
##    860        0.4322             nan     0.0100   -0.0001
##    880        0.4251             nan     0.0100   -0.0000
##    900        0.4184             nan     0.0100    0.0001
##    920        0.4118             nan     0.0100   -0.0002
##    940        0.4050             nan     0.0100   -0.0001
##    960        0.3981             nan     0.0100   -0.0002
##    980        0.3916             nan     0.0100   -0.0001
##   1000        0.3858             nan     0.0100   -0.0000
best_trees <- gbm.perf(gbm_model, method = "cv")

gbm_predictions <- predict(gbm_model, newdata = test_data, n.trees = best_trees)
gbm_mse <- mean((gbm_predictions - y_test)^2)
cat("GBM Mean Squared Error on Test Set:", gbm_mse, "\n")
## GBM Mean Squared Error on Test Set: NA
gbm_importance <- summary(gbm_model)

print(gbm_importance)
##                                         var    rel.inf
## hs_pcb170_cadj_Log2     hs_pcb170_cadj_Log2 7.17452557
## metab_95                           metab_95 7.01343903
## metab_49                           metab_49 6.29708960
## metab_8                             metab_8 3.95379904
## metab_161                         metab_161 3.13067643
## h_cohort                           h_cohort 2.85498639
## metab_163                         metab_163 2.54063347
## hs_pbde153_cadj_Log2   hs_pbde153_cadj_Log2 2.20596365
## metab_26                           metab_26 2.16772212
## hs_dde_cadj_Log2           hs_dde_cadj_Log2 2.11660555
## metab_177                         metab_177 1.84792341
## metab_143                         metab_143 1.79549171
## metab_48                           metab_48 1.75233342
## metab_30                           metab_30 1.67215010
## hs_pfoa_c_Log2               hs_pfoa_c_Log2 1.65769679
## hs_cu_c_Log2                   hs_cu_c_Log2 1.55529425
## metab_142                         metab_142 1.50928543
## metab_47                           metab_47 1.46863592
## metab_120                         metab_120 1.46391164
## metab_160                         metab_160 1.43134372
## metab_141                         metab_141 1.28844230
## metab_59                           metab_59 1.27953690
## metab_171                         metab_171 1.23101024
## metab_6                             metab_6 1.17712040
## metab_50                           metab_50 1.14085803
## metab_94                           metab_94 1.03652607
## metab_115                         metab_115 1.01127946
## metab_96                           metab_96 0.99458189
## metab_154                         metab_154 0.96051941
## hs_pfos_c_Log2               hs_pfos_c_Log2 0.86671736
## metab_122                         metab_122 0.84234437
## metab_146                         metab_146 0.79612293
## metab_78                           metab_78 0.72108650
## metab_128                         metab_128 0.71803369
## metab_110                         metab_110 0.71420291
## hs_hg_c_Log2                   hs_hg_c_Log2 0.71177199
## hs_bakery_prod_Ter       hs_bakery_prod_Ter 0.69131177
## metab_153                         metab_153 0.67376194
## metab_117                         metab_117 0.61954855
## metab_172                         metab_172 0.60951813
## metab_91                           metab_91 0.60873206
## metab_130                         metab_130 0.59565372
## hs_pcb153_cadj_Log2     hs_pcb153_cadj_Log2 0.56883396
## metab_68                           metab_68 0.53475617
## hs_child_age_None         hs_child_age_None 0.49832122
## metab_116                         metab_116 0.49065463
## metab_136                         metab_136 0.49046402
## metab_113                         metab_113 0.48807115
## metab_162                         metab_162 0.44911200
## metab_57                           metab_57 0.44576546
## metab_99                           metab_99 0.44345569
## hs_pfhxs_c_Log2             hs_pfhxs_c_Log2 0.43693720
## metab_55                           metab_55 0.42357257
## hs_co_c_Log2                   hs_co_c_Log2 0.40932149
## hs_mo_c_Log2                   hs_mo_c_Log2 0.40713040
## metab_75                           metab_75 0.40495809
## metab_145                         metab_145 0.40004711
## metab_104                         metab_104 0.38534591
## metab_3                             metab_3 0.38469627
## metab_28                           metab_28 0.36650478
## metab_27                           metab_27 0.34265574
## metab_54                           metab_54 0.32862271
## metab_7                             metab_7 0.32064813
## metab_176                         metab_176 0.30550173
## metab_109                         metab_109 0.29742323
## metab_119                         metab_119 0.29553128
## e3_sex_None                     e3_sex_None 0.29515840
## metab_82                           metab_82 0.29161440
## metab_43                           metab_43 0.28997110
## hs_pb_c_Log2                   hs_pb_c_Log2 0.27731432
## metab_149                         metab_149 0.27206310
## metab_85                           metab_85 0.26465783
## metab_77                           metab_77 0.26342051
## metab_15                           metab_15 0.26152983
## metab_105                         metab_105 0.25676464
## hs_mbzp_cadj_Log2         hs_mbzp_cadj_Log2 0.25337587
## metab_102                         metab_102 0.24703000
## metab_20                           metab_20 0.24434219
## metab_81                           metab_81 0.23967894
## metab_152                         metab_152 0.23833237
## metab_39                           metab_39 0.23817782
## metab_2                             metab_2 0.23556811
## metab_71                           metab_71 0.23553088
## h_bfdur_Ter                     h_bfdur_Ter 0.23440942
## metab_127                         metab_127 0.23353942
## metab_53                           metab_53 0.21051382
## metab_100                         metab_100 0.19692758
## metab_51                           metab_51 0.19375771
## metab_12                           metab_12 0.19315162
## metab_29                           metab_29 0.18782695
## metab_44                           metab_44 0.18591972
## metab_56                           metab_56 0.18159051
## metab_151                         metab_151 0.18050106
## metab_70                           metab_70 0.17974570
## metab_33                           metab_33 0.17844071
## metab_144                         metab_144 0.17736775
## metab_76                           metab_76 0.17525980
## metab_90                           metab_90 0.17370247
## metab_148                         metab_148 0.16970555
## metab_67                           metab_67 0.16965371
## metab_24                           metab_24 0.16822606
## metab_174                         metab_174 0.16308422
## metab_147                         metab_147 0.15895027
## metab_22                           metab_22 0.15292928
## metab_133                         metab_133 0.15211469
## metab_40                           metab_40 0.15157112
## metab_92                           metab_92 0.15074862
## metab_123                         metab_123 0.14888646
## metab_165                         metab_165 0.14807464
## metab_164                         metab_164 0.14731732
## metab_155                         metab_155 0.14499331
## e3_yearbir_None             e3_yearbir_None 0.14418236
## metab_83                           metab_83 0.14172014
## metab_31                           metab_31 0.13709250
## metab_137                         metab_137 0.13339110
## metab_118                         metab_118 0.13234372
## metab_10                           metab_10 0.13230366
## metab_121                         metab_121 0.12935547
## metab_11                           metab_11 0.12858949
## metab_73                           metab_73 0.12689016
## metab_35                           metab_35 0.12243171
## metab_4                             metab_4 0.11884420
## metab_135                         metab_135 0.11534955
## metab_129                         metab_129 0.11186107
## metab_124                         metab_124 0.11146572
## h_edumc_None                   h_edumc_None 0.11049115
## metab_5                             metab_5 0.10784973
## metab_131                         metab_131 0.10516928
## metab_13                           metab_13 0.10255427
## metab_37                           metab_37 0.10180845
## metab_156                         metab_156 0.09890787
## hs_cd_c_Log2                   hs_cd_c_Log2 0.09870967
## metab_173                         metab_173 0.09766258
## metab_106                         metab_106 0.09743478
## metab_65                           metab_65 0.09540889
## metab_61                           metab_61 0.09521138
## metab_170                         metab_170 0.09392339
## metab_97                           metab_97 0.09338812
## metab_88                           metab_88 0.09334622
## metab_157                         metab_157 0.09152121
## metab_64                           metab_64 0.08842711
## metab_38                           metab_38 0.08777233
## metab_23                           metab_23 0.08689099
## metab_60                           metab_60 0.08353259
## metab_41                           metab_41 0.08305904
## metab_159                         metab_159 0.08300417
## metab_93                           metab_93 0.07797704
## metab_111                         metab_111 0.07359432
## metab_139                         metab_139 0.07306725
## metab_52                           metab_52 0.07292251
## metab_103                         metab_103 0.07158258
## metab_25                           metab_25 0.06911508
## hs_cs_c_Log2                   hs_cs_c_Log2 0.06809545
## metab_167                         metab_167 0.06693830
## metab_89                           metab_89 0.06352953
## metab_63                           metab_63 0.06137982
## hs_prpa_cadj_Log2         hs_prpa_cadj_Log2 0.06058699
## metab_69                           metab_69 0.05713214
## hs_mnbp_cadj_Log2         hs_mnbp_cadj_Log2 0.05638747
## metab_79                           metab_79 0.05580534
## metab_14                           metab_14 0.05475433
## metab_45                           metab_45 0.05354158
## metab_46                           metab_46 0.05327852
## metab_98                           metab_98 0.05218432
## h_native_None                 h_native_None 0.05193607
## hs_total_lipids_Ter     hs_total_lipids_Ter 0.05114275
## metab_72                           metab_72 0.04900319
## metab_166                         metab_166 0.04674223
## metab_108                         metab_108 0.04604288
## metab_101                         metab_101 0.04502078
## metab_132                         metab_132 0.04296251
## metab_175                         metab_175 0.03690880
## metab_168                         metab_168 0.03521842
## metab_34                           metab_34 0.03232148
## metab_169                         metab_169 0.03231200
## metab_138                         metab_138 0.03048418
## metab_114                         metab_114 0.02910522
## metab_21                           metab_21 0.02783841
## metab_66                           metab_66 0.02621212
## metab_62                           metab_62 0.02598841
## metab_84                           metab_84 0.02582321
## metab_1                             metab_1 0.02509358
## metab_134                         metab_134 0.02420686
## metab_80                           metab_80 0.02382858
## metab_19                           metab_19 0.02061960
## metab_150                         metab_150 0.02042669
## hs_org_food_Ter             hs_org_food_Ter 0.02023934
## metab_36                           metab_36 0.01926574
## metab_9                             metab_9 0.01803771
## metab_32                           metab_32 0.01711978
## metab_112                         metab_112 0.01698640
## metab_107                         metab_107 0.01680681
## hs_dep_cadj_Log2           hs_dep_cadj_Log2 0.01596550
## metab_140                         metab_140 0.01557540
## metab_87                           metab_87 0.01527845
## metab_16                           metab_16 0.01442643
## metab_86                           metab_86 0.01413670
## hs_total_sweets_Ter     hs_total_sweets_Ter 0.01319851
## hs_mibp_cadj_Log2         hs_mibp_cadj_Log2 0.00000000
## hs_dairy_Ter                   hs_dairy_Ter 0.00000000
## hs_fastfood_Ter             hs_fastfood_Ter 0.00000000
## hs_readymade_Ter           hs_readymade_Ter 0.00000000
## hs_total_bread_Ter       hs_total_bread_Ter 0.00000000
## hs_total_fish_Ter         hs_total_fish_Ter 0.00000000
## hs_total_fruits_Ter     hs_total_fruits_Ter 0.00000000
## hs_total_potatoes_Ter hs_total_potatoes_Ter 0.00000000
## hs_total_veg_Ter           hs_total_veg_Ter 0.00000000
## metab_17                           metab_17 0.00000000
## metab_18                           metab_18 0.00000000
## metab_42                           metab_42 0.00000000
## metab_58                           metab_58 0.00000000
## metab_74                           metab_74 0.00000000
## metab_125                         metab_125 0.00000000
## metab_126                         metab_126 0.00000000
## metab_158                         metab_158 0.00000000

Group LASSO

With Metabolomics

selected_metabolomics_data <- selected_metabolomics_data %>% na.omit()

median_value <- median(selected_metabolomics_data$hs_zbmi_who, na.rm = TRUE)
selected_metabolomics_data$hs_zbmi_who_binary <- ifelse(selected_metabolomics_data$hs_zbmi_who > median_value, 1, 0)

set.seed(101)
trainIndex <- caret::createDataPartition(selected_metabolomics_data$hs_zbmi_who_binary, p = .7, list = FALSE, times = 1)
train_data <- selected_metabolomics_data[trainIndex,]
test_data <- selected_metabolomics_data[-trainIndex,]

train_data_clean <- train_data[complete.cases(train_data), ]
test_data_clean <- test_data[complete.cases(test_data), ]

x_train <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, data = train_data_clean)[, -1]
y_train <- as.numeric(train_data_clean$hs_zbmi_who_binary)

x_test <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, data = test_data_clean)[, -1]
y_test <- as.numeric(test_data_clean$hs_zbmi_who_binary)

num_chemicals <- length(chemicals_selected)
num_diet <- length(diet_selected)
num_metabolomics <- ncol(metabol_serum_transposed) - 1  # Excluding ID
num_covariates <- ncol(outcome_and_cov) - 3  # Excluding ID and outcome

# Combine all the lengths
total_length <- num_chemicals + num_diet + num_metabolomics + num_covariates
cat("Total length of predictors:", total_length, "\n")
## Total length of predictors: 216
cat("Number of predictors in x_train:", ncol(x_train), "\n")
## Number of predictors in x_train: 239
group_indices <- c(
  rep(1, num_chemicals),  # Group 1: Chemicals
  rep(2, num_diet),       # Group 2: Postnatal diet
  rep(3, num_metabolomics), # Group 3: Metabolomics (excluding ID)
  rep(4, num_covariates)  # Group 4: Covariates (excluding ID and outcome)
)

if (length(group_indices) < ncol(x_train)) {
  group_indices <- c(group_indices, rep(5, ncol(x_train) - length(group_indices)))
} else if (length(group_indices) > ncol(x_train)) {
  group_indices <- group_indices[1:ncol(x_train)]
}

cat("Length of group_indices:", length(group_indices), "\n")
## Length of group_indices: 239
cat("Number of columns in x_train:", ncol(x_train), "\n")
## Number of columns in x_train: 239
group_lasso_model <- grplasso(x_train, y_train, index = group_indices, lambda = 0.1, model = LogReg())
## Couldn't find intercept. Setting center = FALSE.
## Lambda: 0.1  nr.var: 239
coef(group_lasso_model)
##                                         0.1
## hs_child_age_None              -0.814555750
## h_cohort2                       3.234390126
## h_cohort3                       4.206670924
## h_cohort4                       1.776110355
## h_cohort5                       3.535594058
## h_cohort6                       0.815805203
## e3_sex_Nonemale                 0.409834794
## e3_yearbir_None2004            -0.343737604
## e3_yearbir_None2005             1.361351042
## e3_yearbir_None2006             1.252469223
## e3_yearbir_None2007             4.146651290
## e3_yearbir_None2008             3.728110763
## e3_yearbir_None2009             6.196278675
## h_edumc_None2                   0.907073602
## h_edumc_None3                   0.616745843
## h_native_None1                  1.857354603
## h_native_None2                  1.201650549
## hs_cd_c_Log2                   -0.028984085
## hs_co_c_Log2                    0.410669666
## hs_cs_c_Log2                    0.354839370
## hs_cu_c_Log2                    0.082330485
## hs_hg_c_Log2                    0.016901788
## hs_mo_c_Log2                   -0.311599261
## hs_pb_c_Log2                    0.508267163
## hs_dde_cadj_Log2                0.016035915
## hs_pcb153_cadj_Log2            -0.768239406
## hs_pcb170_cadj_Log2            -0.038885008
## hs_dep_cadj_Log2               -0.098028508
## hs_pbde153_cadj_Log2           -0.126021425
## hs_pfhxs_c_Log2                 0.205519000
## hs_pfoa_c_Log2                 -0.961203142
## hs_pfos_c_Log2                  0.249979788
## hs_prpa_cadj_Log2              -0.025727699
## hs_mbzp_cadj_Log2               0.131623580
## hs_mibp_cadj_Log2              -0.034664908
## hs_mnbp_cadj_Log2              -0.150898534
## h_bfdur_Ter(10.8,34.9]          0.607301430
## h_bfdur_Ter(34.9,Inf]           0.897256516
## hs_bakery_prod_Ter(2,6]        -0.543308422
## hs_bakery_prod_Ter(6,Inf]      -0.675342550
## hs_dairy_Ter(14.6,25.6]         0.167430517
## hs_dairy_Ter(25.6,Inf]          0.433876848
## hs_fastfood_Ter(0.132,0.5]     -0.610485396
## hs_fastfood_Ter(0.5,Inf]       -0.506487333
## hs_org_food_Ter(0.132,1]        0.571040806
## hs_org_food_Ter(1,Inf]          0.564690937
## hs_readymade_Ter(0.132,0.5]    -0.176643475
## hs_readymade_Ter(0.5,Inf]      -0.066547593
## hs_total_bread_Ter(7,17.5]     -0.888713877
## hs_total_bread_Ter(17.5,Inf]   -0.348798406
## hs_total_fish_Ter(1.5,3]        0.111383056
## hs_total_fish_Ter(3,Inf]        0.154284858
## hs_total_fruits_Ter(7,14.1]     0.172802450
## hs_total_fruits_Ter(14.1,Inf]   0.903091073
## hs_total_lipids_Ter(3,7]        0.625145566
## hs_total_lipids_Ter(7,Inf]      0.807497857
## hs_total_potatoes_Ter(3,4]      0.057915791
## hs_total_potatoes_Ter(4,Inf]   -0.060240223
## hs_total_sweets_Ter(4.1,8.5]   -0.081010725
## hs_total_sweets_Ter(8.5,Inf]    0.216537710
## hs_total_veg_Ter(6,8.5]         0.460212226
## hs_total_veg_Ter(8.5,Inf]      -0.662290016
## metab_1                        -0.311895089
## metab_2                         0.385905761
## metab_3                        -0.292794948
## metab_4                         0.015837471
## metab_5                         1.568182472
## metab_6                         0.574305942
## metab_7                         0.340036221
## metab_8                         1.267953906
## metab_9                        -2.271132612
## metab_10                        1.780824593
## metab_11                        0.270052036
## metab_12                        1.312080337
## metab_13                       -1.063086861
## metab_14                       -5.846754121
## metab_15                        1.284448169
## metab_16                        3.034447155
## metab_17                       -0.971046154
## metab_18                       -3.131430223
## metab_19                       -0.669616989
## metab_20                       -1.828571982
## metab_21                       -0.579589036
## metab_22                        0.355017912
## metab_23                       -0.696581826
## metab_24                        1.182560001
## metab_25                        2.669057609
## metab_26                        0.023886249
## metab_27                        1.432259431
## metab_28                        2.458945586
## metab_29                       -0.613063489
## metab_30                        0.421833304
## metab_31                        0.363846354
## metab_32                       -0.980666345
## metab_33                        0.637697410
## metab_34                       -2.244945408
## metab_35                       -1.188810242
## metab_36                        4.096963657
## metab_37                       -0.527705964
## metab_38                       -0.545066235
## metab_39                       -0.346670443
## metab_40                        1.493529695
## metab_41                       -0.031066113
## metab_42                       -1.350630847
## metab_43                       -0.380572837
## metab_44                        1.481316441
## metab_45                        0.604551202
## metab_46                        0.014126441
## metab_47                        1.975858237
## metab_48                       -4.317396889
## metab_49                        1.436981843
## metab_50                       -0.190934466
## metab_51                        1.155716784
## metab_52                        4.708869058
## metab_53                       -0.791295980
## metab_54                        1.613455004
## metab_55                        2.166599257
## metab_56                        0.016602408
## metab_57                       -4.776328063
## metab_58                        4.491685733
## metab_59                       -0.888365162
## metab_60                        3.863561909
## metab_61                       -6.789042293
## metab_62                        7.303445379
## metab_63                       -0.973589444
## metab_64                        0.569662598
## metab_65                       -4.591725795
## metab_66                        0.122419072
## metab_67                       -2.570017083
## metab_68                        1.738365943
## metab_69                        2.301012623
## metab_70                        1.706530275
## metab_71                       -2.785950856
## metab_72                       -0.385208189
## metab_73                       -1.081375044
## metab_74                       -1.775137739
## metab_75                        0.173707111
## metab_76                        1.434844610
## metab_77                        0.084220664
## metab_78                        1.470554306
## metab_79                        0.549792988
## metab_80                        5.150695314
## metab_81                        1.405265784
## metab_82                      -15.557083256
## metab_83                        1.907768517
## metab_84                       -2.033370533
## metab_85                       -3.767492824
## metab_86                        2.972664416
## metab_87                        7.153643275
## metab_88                        1.542898311
## metab_89                      -11.095434459
## metab_90                       10.024855247
## metab_91                        1.739097254
## metab_92                       -0.331808414
## metab_93                       -4.910208969
## metab_94                       -0.009741673
## metab_95                        9.342542793
## metab_96                        1.654759735
## metab_97                       -0.204267915
## metab_98                       -3.986788931
## metab_99                       -3.172587132
## metab_100                       0.409309495
## metab_101                      -2.339092968
## metab_102                      -3.031017996
## metab_103                       0.210266938
## metab_104                       2.964893529
## metab_105                      -0.595306702
## metab_106                      -0.766434869
## metab_107                       2.862769887
## metab_108                       1.702309555
## metab_109                      -0.143626106
## metab_110                      -0.020270609
## metab_111                      -4.721917618
## metab_112                      -0.969457396
## metab_113                       5.388124706
## metab_114                       8.276250166
## metab_115                       1.171360332
## metab_116                      -3.714496932
## metab_117                       1.392841523
## metab_118                      -6.861578166
## metab_119                      -2.335442309
## metab_120                      -0.708993007
## metab_121                       2.477920128
## metab_122                      -5.222147710
## metab_123                       7.336050211
## metab_124                       7.602248915
## metab_125                      -2.264330502
## metab_126                       0.243967092
## metab_127                      -0.458168685
## metab_128                       1.667698083
## metab_129                       0.263101733
## metab_130                      -8.145832818
## metab_131                      -6.342202995
## metab_132                      -2.801368265
## metab_133                      -4.939903271
## metab_134                       3.990753266
## metab_135                      -5.200872081
## metab_136                      -1.494972615
## metab_137                       2.988221954
## metab_138                       6.449970477
## metab_139                       1.353776081
## metab_140                       0.687405421
## metab_141                      -3.654939081
## metab_142                       0.118262553
## metab_143                      -0.032516439
## metab_144                       5.062581105
## metab_145                      -1.767286794
## metab_146                      -1.322711932
## metab_147                      -0.025789862
## metab_148                       0.420414611
## metab_149                      -0.414900107
## metab_150                       0.688680892
## metab_151                      -0.019549962
## metab_152                      -0.309537563
## metab_153                      -0.778355554
## metab_154                       0.163924677
## metab_155                      -5.404627485
## metab_156                       1.525679547
## metab_157                      -1.781301886
## metab_158                       2.921214188
## metab_159                      -0.096156986
## metab_160                      -9.279626651
## metab_161                      12.730750032
## metab_162                       5.008959913
## metab_163                      -3.686396371
## metab_164                      -0.283334399
## metab_165                       2.695548788
## metab_166                      -3.095310226
## metab_167                      -0.339090909
## metab_168                      -0.804367234
## metab_169                      -0.868436696
## metab_170                      -0.509452215
## metab_171                      -0.877797504
## metab_172                      -1.147410567
## metab_173                       3.205560239
## metab_174                      -1.989846072
## metab_175                      -2.670777766
## metab_176                       0.903437525
## metab_177                       1.295496261
group_lasso_predictions <- predict(group_lasso_model, newdata = x_test, type = "response")
# convert probabilities to binary predictions
binary_predictions <- ifelse(group_lasso_predictions > 0.5, 1, 0)

accuracy <- mean(binary_predictions == y_test)
cat("Group LASSO Accuracy on Test Set:", accuracy, "\n")
## Group LASSO Accuracy on Test Set: 0.7094972
conf_matrix <- confusionMatrix(factor(binary_predictions), factor(y_test))
conf_matrix
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 125  50
##          1  54 129
##                                          
##                Accuracy : 0.7095         
##                  95% CI : (0.6595, 0.756)
##     No Information Rate : 0.5            
##     P-Value [Acc > NIR] : 6.51e-16       
##                                          
##                   Kappa : 0.419          
##                                          
##  Mcnemar's Test P-Value : 0.7686         
##                                          
##             Sensitivity : 0.6983         
##             Specificity : 0.7207         
##          Pos Pred Value : 0.7143         
##          Neg Pred Value : 0.7049         
##              Prevalence : 0.5000         
##          Detection Rate : 0.3492         
##    Detection Prevalence : 0.4888         
##       Balanced Accuracy : 0.7095         
##                                          
##        'Positive' Class : 0              
## 
# ROC Curve and AUC
roc_curve <- roc(y_test, group_lasso_predictions)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for Group LASSO Model (with metabolomics)")

auc_value <- auc(roc_curve)
cat("Group LASSO AUC on Test Set:", auc_value)
## Group LASSO AUC on Test Set: 0.7683593

Without Metabolomics

finalized_data <- finalized_data %>% na.omit()

median_value <- median(finalized_data$hs_zbmi_who, na.rm = TRUE)
finalized_data$hs_zbmi_who_binary <- ifelse(finalized_data$hs_zbmi_who > median_value, 1, 0)

set.seed(101)
trainIndex <- createDataPartition(finalized_data$hs_zbmi_who_binary, p = .7, list = FALSE, times = 1)
train_data <- finalized_data[trainIndex,]
test_data  <- finalized_data[-trainIndex,]

train_data_clean <- train_data[complete.cases(train_data), ]

x_train <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, data = train_data_clean)[,-1]
y_train <- as.numeric(train_data_clean$hs_zbmi_who_binary)

test_data_clean <- test_data[complete.cases(test_data), ]

x_test <- model.matrix(hs_zbmi_who_binary ~ . - hs_zbmi_who, data = test_data_clean)[,-1]
y_test <- as.numeric(test_data_clean$hs_zbmi_who_binary)

num_chemicals <- length(chemicals_selected)
num_diet <- length(diet_selected)
num_covariates <- ncol(outcome_and_cov) - 2  # excluding outcome and binary outcome

total_length <- num_chemicals + num_diet + num_covariates

group_indices <- c(
    rep(1, num_chemicals),  # Group 1: Chemicals
    rep(2, num_diet),  # Group 2: Postnatal diet
    rep(3, num_covariates)  # Group 3: Covariates (excluding outcome)
)

length(group_indices) == ncol(x_train)
## [1] FALSE
# adjust length if necessary
if (length(group_indices) < ncol(x_train)) {
    group_indices <- c(group_indices, rep(4, ncol(x_train) - length(group_indices)))
}

length(group_indices) == ncol(x_train)
## [1] TRUE
group_lasso_model <- grplasso(x_train, y_train, index = group_indices, lambda = 0.1, model = LogReg())
## Couldn't find intercept. Setting center = FALSE.
## Lambda: 0.1  nr.var: 60
group_lasso_coef <- coef(group_lasso_model)
print(group_lasso_coef)
##                                        0.1
## e3_sex_Nonemale                0.215800640
## e3_yearbir_None2004           -0.313105353
## e3_yearbir_None2005            0.147831260
## e3_yearbir_None2006            0.399591772
## e3_yearbir_None2007            0.662232475
## e3_yearbir_None2008            0.820956883
## e3_yearbir_None2009            1.535090138
## h_edumc_None2                  0.357957282
## h_edumc_None3                  0.332942693
## h_cohort2                      1.769290964
## h_cohort3                      1.861416323
## h_cohort4                      1.289192363
## h_cohort5                      0.736127336
## h_cohort6                      0.819950804
## hs_child_age_None             -0.251413569
## h_bfdur_Ter(10.8,34.9]         0.022481336
## h_bfdur_Ter(34.9,Inf]          0.421746681
## hs_bakery_prod_Ter(2,6]       -0.367140841
## hs_bakery_prod_Ter(6,Inf]     -0.665749368
## hs_dairy_Ter(14.6,25.6]        0.176559184
## hs_dairy_Ter(25.6,Inf]        -0.081425257
## hs_fastfood_Ter(0.132,0.5]     0.121228175
## hs_fastfood_Ter(0.5,Inf]       0.067584836
## hs_org_food_Ter(0.132,1]       0.103549297
## hs_org_food_Ter(1,Inf]         0.072419958
## hs_readymade_Ter(0.132,0.5]   -0.025717192
## hs_readymade_Ter(0.5,Inf]      0.003605485
## hs_total_bread_Ter(7,17.5]    -0.227202592
## hs_total_bread_Ter(17.5,Inf]  -0.145018021
## hs_total_fish_Ter(1.5,3]      -0.037890718
## hs_total_fish_Ter(3,Inf]       0.198059213
## hs_total_fruits_Ter(7,14.1]    0.188427962
## hs_total_fruits_Ter(14.1,Inf]  0.167196028
## hs_total_lipids_Ter(3,7]      -0.146801779
## hs_total_lipids_Ter(7,Inf]    -0.187460509
## hs_total_potatoes_Ter(3,4]    -0.021779148
## hs_total_potatoes_Ter(4,Inf]  -0.017630035
## hs_total_sweets_Ter(4.1,8.5]  -0.200656559
## hs_total_sweets_Ter(8.5,Inf]  -0.011508070
## hs_total_veg_Ter(6,8.5]        0.069869371
## hs_total_veg_Ter(8.5,Inf]     -0.142810762
## hs_cd_c_Log2                  -0.008229695
## hs_co_c_Log2                   0.009914760
## hs_cs_c_Log2                   0.393405877
## hs_cu_c_Log2                   0.456205069
## hs_hg_c_Log2                   0.009165825
## hs_mo_c_Log2                  -0.207038128
## hs_pb_c_Log2                  -0.162471124
## hs_dde_cadj_Log2              -0.150863328
## hs_pcb153_cadj_Log2           -0.742048287
## hs_pcb170_cadj_Log2           -0.103155838
## hs_dep_cadj_Log2              -0.042837953
## hs_pbde153_cadj_Log2          -0.056592257
## hs_pfhxs_c_Log2                0.091695788
## hs_pfoa_c_Log2                -0.354839120
## hs_pfos_c_Log2                 0.022225709
## hs_prpa_cadj_Log2             -0.023211134
## hs_mbzp_cadj_Log2              0.175002499
## hs_mibp_cadj_Log2             -0.115639713
## hs_mnbp_cadj_Log2             -0.089607981
group_lasso_predictions <- predict(group_lasso_model, newdata = x_test, type = "response")
binary_predictions <- ifelse(group_lasso_predictions > 0.5, 1, 0)

accuracy <- mean(binary_predictions == y_test)
cat("Group LASSO Accuracy on Test Set:", accuracy, "\n")
## Group LASSO Accuracy on Test Set: 0.6512821
conf_matrix <- confusionMatrix(factor(binary_predictions), factor(y_test))
conf_matrix
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 129  76
##          1  60 125
##                                           
##                Accuracy : 0.6513          
##                  95% CI : (0.6017, 0.6986)
##     No Information Rate : 0.5154          
##     P-Value [Acc > NIR] : 4.022e-08       
##                                           
##                   Kappa : 0.3037          
##                                           
##  Mcnemar's Test P-Value : 0.1984          
##                                           
##             Sensitivity : 0.6825          
##             Specificity : 0.6219          
##          Pos Pred Value : 0.6293          
##          Neg Pred Value : 0.6757          
##              Prevalence : 0.4846          
##          Detection Rate : 0.3308          
##    Detection Prevalence : 0.5256          
##       Balanced Accuracy : 0.6522          
##                                           
##        'Positive' Class : 0               
## 
roc_curve <- roc(y_test, group_lasso_predictions)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc_curve, main = "ROC Curve for Group LASSO Model (without metabolomics)")

auc_value <- auc(roc_curve)
cat("Group LASSO AUC on Test Set:", auc_value, "\n")
## Group LASSO AUC on Test Set: 0.7146279